According to Turkish outlet Asist Analiz, the two Premier League clubs are keen to sign the 24-year-old, who scored a staggering 33 goals while on loan at Trabzonspor last season.
Sorloth was due to complete a move to RB Leipzig on Monday but his medical with the German club was cancelled at the last minute, the report adds.
Jose Mourinho has made it no secret that he is in the market for a new striker to provide back-up to Harry Kane.
However, negotiations to sign Sorloth will be complicated as his loan at Trabzonspor does not expire until the end of the 2020/21 campaign
Gareth Bale completed his return to Spurs on Saturday, signing a season-long loan from Real Madrid where he spent the last seven years, while Sergio Reguilon also arrived from Los Blancos on a permanent contract.
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And Bale is confident Mourinho can deliver trophies to Spurs and is looking forward to working with the manager who tried to sign him twice previously.
"I spoke to him prior to coming over obviously when we were speaking," Bale said on BT Sport. "He's spoken to me about a few positions that he would like me to play and obviously I'm happy with that.
"Obviously he's a big key incumbent, he's a household name, he's a winner and I think he's the perfect fit for Tottenham.
"We all want to win trophies and he knows how to better than anyone so hopefully this season can be that season. What every Tottenham fan wants is a trophy so we'll be trying as hard as we can in every competition to do that."
Manchester United and Tottenham are battling it out to sign Crystal Palace striker Alexander Sorloth, reports claim.