Under the plan, the EU could raise more revenues directly from member states' taxes, which constitute about 10 per cent of its total budget.
Currently, national payments to the EU budget are based on the countries' wealth.
The EU is keen to find alternative revenues, especially in view of the planned exit of the UK, one of the largest contributors to its budget, following its 23 June referendum.
The current EU budget, totalling around one trillion euros, runs from 2014 till 2020 inclusive.
The plans were spelled out by the former European Commissioner Mario Monti, who chairs the advisory group and who suggested increasing the share of EU revenues coming from taxes at the expense of the payments from national budgets.
He also proposed a direct link between taxes raised at the national level and spending on specific policies, such as security.
Monti, a former Italian Prime Minister, said the advisory group was studying the possibility of raising funds from national taxes on motor fuel, financial activities or carbon emissions.
Monti said, "There are certainly ways to devise 'own resources' (EU revenues) linked to an objective, a priority or a policy. This would make the financing of the EU more understandable to our citizens."
He also countered suggestions that the move could be seen as "EU meddling" in taxation, traditionally a closely-guarded national competence.
"There is no reason why some decisions on taxation should be outside the reach of the EU," said Monti.
French centre right MEP Alain Lamassoure, the EPP group representative on the advisory group, said that Brexit would "force" the EU to reform the way it is funded in future.
This was, he said, partly because some 80 per cent of the budget is funded by national contributions and the EU was about to lose one of its biggest contributors.
"There has to be reform. Because of the lack of own resources, the European budget is condemned to funding the priorities of yesterday to the detriment of the needs of today and tomorrow."
Lamassoure said, "We must assure taxpayers that each euro spent at European level will save more at national level which will result in greater efficiency. This is the budgetary translation of the subsidiarity principle."
He also denied that raising more funds from national taxes represented a further "power grab" by the EU, adding, "Under the plans we are proposing there will be no loss of fiscal sovereignty."
Last week, Monti and Lamassoure joined European budget and human resources Commissioner Kristalina Georgieva, as well as other MEPs and representatives of national parliaments, to discuss how to finance the roughly €145bn annual EU budget.
Monti said his group was studying the possibility of raising funds from national taxes on motor fuel, financial activities or carbon emissions.
The advisory group's non-binding suggestions, which are to be finalised in a report due in December, could reduce transfers made by member states to the EU budget.
As many member states encounter difficulties consolidating their budgets and the UK, one of the net payers, is about to leave, the question of the future financing of the EU is becoming more prominent.
The two-day "inter-institutional conference on the future financing of the European Union" event was designed to help resolve such issues.
Participants discussed the role of the EU budget, the advantages and shortcomings of existing instruments or ways to strengthen coherence between national and European budgets.
Commission President Jean-Claude Juncker is expected to push for changes to the stability and growth pact in his state of the union speech to MEPs in Strasbourg on Wednesday by calling for more flexibility when assessing the deficit and debt of EU countries.
Juncker told Commissioners at their recent retreat in Knokke he was considering calling for education and investment spending to be excluded from the EU countries' budget deficit and debt calculations.
Elsewhere, French Socialist MEP Isabelle Thomas said, "We are facing many challenges, and an important one is the EU budget. We are all tired of the Council announcing that we share the same priorities on this or that project, without ever unlocking any financing.
"We must find the resources to welcome refugees, ensure safety at the EU's borders, fill Europe's €600bn investment gap and support research. However, we must not do so at the expense of other political priorities, such as fighting youth employment, as well as cohesion and the CAP."
The EU's budget for next year will be decided over the coming months. The budgets committee will draft a recommendation to MEPs which will be put to a plenary vote at the end of October.
The Commission has proposed an EU budget of €134.9bn in payments and €157.7bn in commitments for next year. Commitments are what the EU undertakes to spend on programmes and may span more than one year, while payments are the actual expenditure foreseen for the next 12-month period.
However, Council wants to cut the budget for commitments by €1.3bn (-0.81 per cent) and for payments by €1.1bn (-0.82 per cent).
According to Parliament, the budget priorities should continue to tackle the migration crisis while helping the economy recover.
Thomas, a Vice-Chair of Parliament's S&D group, added, "The cuts in next year's budget requested by the Council are unacceptable.
"We must address budgetary issues seriously, starting by revising the multiannual financial framework for 2014-2020. We need to urgently put in place our own resources, such as a common tax on multinationals.
"We cannot carry on with a budget worth one per cent of our GDP, while our citizens await concrete answers."