The deadline was put forward as part of the governing body's guidelines on eligibility principles for 2020-21 UEFA club competitions.
Following a meeting of its executive committee last week, UEFA strongly recommended all leagues on hold due to the coronavirus pandemic be completed where possible.
It proposed top divisions could be seen out with a different format, or, where resumption is not feasible, national associations could decide places for next season's continental competitions "on sporting merit".
UEFA expects all leagues to have a plan in place for how they will proceed ahead of the next executive committee meeting on 27 May.
The organisation's guidelines read: "National associations and/or leagues should be in a position to communicate to UEFA by May 25, 2020 the planned restart of their domestic competitions including the date of restart and the relevant competition format.
"In the event that a domestic competition is to be prematurely terminated for legitimate reasons in accordance with [conditions set out by the executive committee], UEFA would require the national association to explain by May 25, 2020 … the special circumstances justifying such premature termination and to select clubs for UEFA club competitions 2020-21 on the basis of sporting merit in the 2019-20 domestic competitions."
Bundesliga clubs have returned to training and could be back on the pitch from May 9, while Serie A teams are expected to be able to practice together the following week.
The situation remains unclear in the Premier League, LaLiga and Ligue 1.
After professional sports were banned in the Netherlands until September 1, the Eredivisie announced the cancellation of its 2019-20 season last week.
No champions were declared and there was no promotion or relegation, with European qualification determined by the table when the league was suspended.
KNVB Beker finalists Utrecht consequently missed out on a place in the Europa League qualifiers and stated they intended to legally challenge the ruling.