The team have hovered above the Premier League relegation zone for long periods of the campaign, but the 3-1 win against Liverpool on Sunday ensured a sixth season in the top flight.
Swansea are hoping for new investment with American businessmen Jason Levien and Steve Kaplan leading a consortium that is in talks to buy a 60% stake in the club.
Coventry City player Ricketts says while Rodgers would be a good choice to take over, Swansea must buck their historic trend and spend big sums in the transfer market if they are to push on next season.
“I think Rodgers still regards himself as a top manager, but he needs to prove that again,” said Ricketts of the man who first took charge there in 2010.
“And I think that’s probably what Swansea need.
“They need not only a manager, but players who have got something to prove, something to aim for and I think Brendan can hopefully not only keep Swansea where they are, but also lift them to the next level again.”
Ricketts added: “It goes against their philosophy a bit, but they need to go and spend between £15-20m on a forward and then probably another £10m or so on two or three other players just to give the squad a lift as much as lift the quality as well.”