The right-back did not put a foot wrong during his loan spell at Schalke last season and impressed all at the club during his stay in the Bundesliga.
Schalke are keen to take him back but they are not in a financial state to sign the defender on a permanent deal from Everton this summer.
It emerged last month that Schalke have not given up on the hope of landing Kenny on another loan deal in the ongoing transfer window.
And according to German broadcaster Sport1, the Bundesliga giants are in indeed in conversations with Everton to probe the possibility of signing Kenny again this summer.
Schalke are interested in taking the defender on another season-long loan deal from Everton ahead of the new season.
Everton would prefer to sell but for the moment they do not have any concrete offers for him for a permanent move away from Goodison Park.
If Kenny stays at the club next season, he is likely to play second fiddle to Seamus Coleman and Everton are also believed to be interested in signing a new right-back.
The 23-year-old is believed to be keen on the move to Schalke, where he is guaranteed to be a starter and play regular football.
Everton are yet to take a call on his future but Schalke are pushing them to make a decision on Kenny soon.