Sorloth, who has also previously been linked with Manchester United, has only scored once in 20 appearances for Palace since joining the Premier League club from FC Midtjylland in January 2018.
The Norway international was in excellent form during a loan spell at Trabzonspor last season, though, netting 33 goals and providing 11 assists in 49 appearances for the Turkish outfit.
According to Football Insider, Spurs had wanted to secure a deal for the striker this summer, but RB Leipzig have won the race to sign him in a move that could be worth more than £20m.
Mourinho's side started their 2020-21 Premier League season with a 1-0 loss at home to Everton on Sunday. body check tags ::