Yilmaz has attracted attention from the likes of Arsenal and Manchester United as he spearheads Galatasaray's assault on the Super Lig title.
The Turkish giants sit five points clear of second placed Besiktas at the top of the league table, and Yilmaz is the Super Lig's joint top scorer with 14 goals so far.
The report claims Arsene Wenger is considering a move for another forward at the end of the season, as Olivier Giroud and Lukas Podolski have struggled to fill the void left by Robin Van Persie.
But Galatasaray president Unal Aysal has looked to ward off interest from the north London club by insisting it would take a massive offer to lure Yilmaz away from Turkey.
He said: "We have not received any offers for Burak Yilmaz, but of course [the speculation] will mount as the end of the season nears closer.
"Burak is a very valuable star for us. If, however, we are talking about Falcao being worth €55m [£48m] then my player is €40m [£35m].
The report claims Yilmaz suggested in January that he would be open to a move to the Premier League, but the Turkey striker stayed with Galatasaray as the transfer window shut.
The Turkish club face a tough test in the Champions League, after their 1-1 home draw against Schalke in the first-leg.
Arsenal likewise, face a battle to progress to the quarter-finals after a 3-1 home defeat to Bayern Munich.
And the Gunners' potential failure to qualify for next year's Champions League could count against them when it comes to signing players like Yilmaz.
Galasataray look odds-on to finish top of their domestic league, granting them entry to next year's competition. But Arsenal, after last weekend's 2-1 derby defeat to Totteham, sit fifth in the Premier League and face an uphill battle to qualify.