Uefa president Aleksander Ceferin is trying to change his own rule to remain in power until 2031.
Ceferin was elected in 2016, replacing Michel Platini, and one of reforms he put in place was a three-term limit for all executive appointments.
He is due to step down in 2027 but the Slovenian’s supporters are working on a plan to amend the rule.
If it was put in place, Ceferin, who was unopposed when he was re-elected this year, could stand again in 2027.
Former Manchester United chief executive David Gill, a member of Uefa’s executive committee, is leading the opposition to any change.
The amendment, which his supporters want as Ceferin took over part-way through Platini’s four-year term in office, would mean any appointment before 2017 would not be counted as part of the allowable three terms.
The matter was raised at an executive committee meeting last week, when Gill is understood to have reacted angrily, arguing the plan was undemocratic. Others at the meeting also voiced their opposition, although it is not known if Ceferin, who has huge support in eastern Europe, has enough wider backing to push through his controversial plan.
The proposal is due to go before Uefa’s congress in Paris on 8 February, when it will need a two-thirds majority of the organisation’s 55 members for the relevant statutes to be amended.
In a statement, Uefa said on Monday: “The legal committee proposed a number of changes to the statutes which clarify some existing provisions to ensure that none are applicable retroactively – in line with a basic legal principle. Both the governance committee and the executive committee approved the changes which will now be considered by congress in February.”