The 25-year-old frontman has been scoring goals for fun for both club and country this season, and has caught the eye of the Premier League top two.
Arsene Wenger has identified the forward as the man to act as back up to Olivier Giroud, while Brendan Rodgers is looking for another striker to support Luis Suarez and Daniel Sturridge after being left disappointed with the form of summer signing Iago Aspas.
The striker has managed 22 goals for both club and country this season, and may be available in January for as little as £7.5million.
“If he keeps on doing well, it will be hard to keep him,” Olympiakos coach Jose Miguel Michel said.
“We’ve known for some time that there has been interest from many clubs, but that’s only logical considering how well he has been doing lately.”
Mitroglou is currently playing alongside Arsenal loanee Joel Campbell at the Greek champions, a fact Wenger may look to use to his advantage when it comes to tempting the forward to north London.
Premier League high flyers Newcastle United are also understood to be monitoring the situation, but know they will face a tough task to beat Arsenal and Liverpool to the forward’s signature.