Forlan’s team lost 2-0 at home to Wanderers on Sunday, their second defeat in four games.
“It’s time to leave Penarol,” he tweeted. “I have no complaints, that’s football.”
The Montevideo club currently languish in seventh place in the 16-team first division, six games after the league restarted following a five-month hiatus caused by the coronavirus pandemic.
They have won only four times since Forlan, a former Penarol and Uruguay striker, was appointed to his first managerial post last December.