Leicester City have also been linked with a move for the striker.
The striker has been in fine form for the Portuguese side this past season, with 31 goals in 44 appearances in all competitions.
They are not the only ones reportedly keen either, with Gianluca di Marzio claiming that Premier League champions Leicester City were another team tracking the forward.
Should a firm offer be made, it seems Slimani's current club are determined to earn a big fee for him, with his manager saying €30m is nothing for his star man.
"I would like for Slimani to stay.," Jesus told SIC Noticias.
"I know it's important that Slimani continues, but also that it is important to sell a player for 30 million euros. At present, 30 million for a player like Slimani is nothing."
From a Tottenham perspective at least, a move for Slimani would certainly make sense this summer.
Mauricio Pochettino’s side are short on numbers up front, relying heavily on Harry Kane to score the goals in the side.
But whether they are willing to spend big money for a player who would likely be on the bench more often than not remains to be seen.