Swansea boss Rodgers takes his side to Goodison Park with them lying a solid 12th in the Premier League, and they will be hoping to record an elusive first away win of the season after their backs-to-the-wall effort in Saturday's goalless draw at Newcastle.
The Welsh club are two places above Everton in the table, with the Toffees having endured a frustrating campaign, particularly at home where they have taken just eight points from their eight home games.
But Rodgers believes that the former Preston boss has what it takes to be successful with one of the Premier League`s elite, saying: "David has done an outstanding job to keep them up the top end of table for so many years. I have an immense respect for David and the job he has done has been remarkable.
"He is a manager who deserves a crack at a club regularly challenging for trophies. He has been one of the most consistent managers over a number of years and he is a great role model for young coaches and managers.
"He was at Preston and did well and got the opportunity at Everton and he has been supported well by an excellent chairman. They don't have resources of their counterparts across the way but he has made them competitive and he is a manager who deserves an opportunity to win trophies."