The Whites defender believes certain players over-exerted this season.
And Bamba feels the pair could have done with a break.
Discussing Leeds' promotion chances next season, the Ivorian told the Yorkshire Evening Post: "Players like Charlie Taylor and Cooky, they’ve played a lot of games and sometimes you need a break.
"If we double up in every position then we’d have a good chance."
After Mirco Antenucci confirmed his departure at the weekend, Leeds have only one player, young goalkeeper Bailey Peacock-Farrell, out of contract this summer, meaning that, in theory, the club has a strong base from which to build.
However, with the future of White head coach Steve Evans uncertain, any hope of stability may take a hit in the coming weeks.
Assuming Peacock-Farrell, who the report claims will hold further contract talks this week, extends his stay at Elland Road, Leeds would have 22 first-team players on their books from July 1 - though Tommaso Bianchi could sign a permanent deal with Ascoli.
However, three of these would be goalkeepers, with Bianchi among seven recognised central midfielders.
As it stands, Taylor is the club's only senior left-back, while their shortage of strikers is perhaps another area of concern.