Former Tottenham Hotspur manager David Pleat does not believe replacing Garry Monk would guarantee a change in Swansea City's fortunes.
Swansea boss Monk has faced increasing scrutiny after only one win in 10 league matches.
Monk says he has the "full backing" of the club's chairman Huw Jenkins and Pleat says the Welsh club should stick with their manager.
"How can they be sure by making a change anything will improve?" he said.
"I think he'll improve himself because he's proved already that he knows how to play good football and the players have responded.
"If there are any personal situations behind the scenes, I don't know, but I'm not prepared to believe everything we are being told by the media."
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Sunday's 1-0 defeat by Liverpool left Swansea 15th in the table and four points above the relegation zone.
Monk insists his side, who host second placed Leicester City on Saturday, will not be dragged into a fight for Premier League survival.
Goalkeeper Lukasz Fabianski says their efforts at Anfield underlined the players' desire to "get results" for Monk.
Pleat, the longest serving member of the League Managers Association committee and who also managed Leicester City, Luton Town and Sheffield Wednesday, believes Swansea can maintain their Premier League status at the end of the season.
"The results, and consistently it's a results based situation, haven't been good," he told BBC Radio Wales Sport.
"But I think he's [Monk] done pretty good work since he's been there, I don't think there's any doubt about that.
"I think they will be alright this season and even if they to finish in their lowest position for two or three years, so be it they'll have to live with that," Pleat added.
"No one's got a divine right to be in the top 10, it's a hard league."
Swansea City Supporters Trust are hopeful Monk can turn around the team's poor form but admit they are concerned by recent results.
The Trust own 21% of the Premier League club and their vice-chairman Jim White said Monk is at least being given the chance to try and turn things around.
"Everyone knows football is a results business and Garry knows that himself," White told BBC Radio Wales Sport.
"I know the chairman and the board are concerned about the results but they've given Garry their support to get through this tough time."