Olejnik, 25, only joined the Gulls last summer from Falkirk and kept 20 clean sheets as Torquay made the League Two play-offs.
Posh are on the look-out for a new first-choice keeper after both Joe Lewis and Paul Jones left the club this summer, and it appears Olejnik is the man they want.
"Peterborough have made three enquiries in all for Bobby," Gulls boss Martin Ling told BBC Radio Cambridgeshire. "He is the best stopper I've ever worked with."
Olejnik signed a new contract until 2014 in February at Plainmoor, which puts Torquay in a strong bargaining position as they look to hold on to their star man.
