The leader of the UK Conservative MEPs, Ashley Fox, has submitted an amendment to the revised rules of procedure being drawn up by Parliament's constitutional affairs committee.
Fox has suggested limiting the Parliament presidency to two terms, as a way of promoting "fresh leadership."
Schulz is preparing to seek re-election for an unprecedented third term.
The German MEP is believed to be seeking to continue in the post beyond January 2017, when he was supposed to step down as part of a "gentlemen's agreement" between the EPP and S&D groups.
Some senior political figures, including the Socialist leader, Italian MEP Gianni Pittella, and European Commission President Jean-Claude Juncker, are believed to support his continued presidency.
Juncker publicly said recently this would provide "stability" for the EU.
There is also opposition to all three EU presidencies being held by centre-right politicians (the European Council President Donald Tusk and Juncker are both EPP members).
But others, including the EPP, want a new President to complete the second half of the current legislative term.
Fox pointed out that introducing a limit would bring the presidency into line with the presidency of the European Council, currently held by Tusk, which allows an individual to serve a maximum of two, two-and-a-half year terms.
He said: "At a time when we are criticising the concentration of power within a number of countries around the world, we feel that this amendment would not only promote fresh leadership but also showcase the democratic values of this House and encourage checks and balances on one of our most visible representatives.
"Of course, another positive affect would be to disqualify Martin Schulz from running for the position again."