The 24-year-old Croatian has been a big part of his national team's World Cup campaign this summer, playing four times and scoring once - his country's opening goal against Argentina, after a calamitous error by Willy Caballero.
Rebic moved from his native Croatia to Italian side Fiorentina in 2013, but only made eight league appearances after being farmed out on loan a number of times.
The past two seasons, Rebic had been loaned out to Frankfurt, where he reunited with former Croatian national team manager Niko Kovac.
He made 49 league appearances and scored eight times during his two years on loan at Frankfurt, and the German club made the move permanent this summer for a reported £1.8m fee.
Rebic and Frankfurt won the DFB-Pokal, Germany's primary cup competition, last season, beating Bayern Munich in the final.
Following another good season in German football and an impressive World Cup showing, a number of top European clubs have started looking more closely at a move for the Split-born left winger.
Rebic is understood to prefer a move to Bayern Munich out of the interested clubs, in order to link up with former boss Kovac once more.
However, Sport Bild suggest Rebic would prefer a move to Bayern Munich to link up again with his former boss in Frankfurt -- Niko Kovac, who he also worked with in charge of Croatia.— Mark Lovell (@LovellLowdown) July 10, 2018
Croatia assistant manager, and ex-Bayern striker, Ivica Olic said: "Ante is someone for Bayern. He could learn from Ribery and replace him in a year. He is ready for a big club."
However, Kovac is expected to be reluctant to sign Rebic at any cost - only agreeing a deal if the fees are favourable to the Bavarian side.
Since Frankfurt are reported to be mooting a €50m starting price, a move to England is understood to be the more likely option should Rebic leave Frankfurt this summer.
Rebic's powerful and robust playing style would also likely be greater appreciated in England's Premier League than in the Bundesliga.