The 29-year-old centre-back has two years left on his Leicester contract, but he was a bit part player last season and did not play a single league game following a one-minute appearance against West Ham on 13th February.
There are question marks over his future at Leicester, with suggestions that the Dane could be on the move this summer.
Several teams in the Premier League have been keeping tabs on him and Thomas Frank wants to take him to Brentford in the ongoing window.
But according to Danish outlet BT, Leicester have rejected an approach for Vestergaard from the London side.
Leicester are yet to sign any players this summer and Brendan Rodgers is believed to be unwilling to weaken his squad without assurances of replacements.
Vestergaard is also yet to push for an exit from the King Power Stadium as well.
It remains to be seen whether Brentford make another effort to snare the defender away from Leicester.
The Dane has returned to pre-season training with Leicester and is believed to be looking forward to the new season.
