Stoke captain Ryan Shawcross is hoping the club can make a quick managerial appointment.
Stoke only signed Lambert for the last couple months of the season, when they were already in the relegation zone.
But his failure to herald an improvement in results could see him part ways with the club.
Shawcross wants a decision made quickly.
"Manager-wise, I think it needs to be resolved this week," said Shawcross to Stoke on Trent Live.
"The club needs to decide who the manager is and, if it is Paul Lambert, we all need to get behind him, move forward and hopefully get back in the Premier League.
"We showed (at Swansea) how much we like him and respect him as a manager, but ultimately it's the club's decision what happens."