MacAnthony took to Twitter after the club rejected the request on Wednesday and said the club will reject any further advances.
According to reports Tomlin had previously spoken with manager Darren Ferguson and director of football Barry Fry in the build-up to submitting his request.
MacAnthony tweeted: "Obviously L Tomlin's agent has been speaking to the press as all classy agents like him do. He is not for sale & any transfer request is turned down.
"That's all I'll say on the Tomlin matter except to say I'm looking forward to seeing him helping our squad challenge for title this season."
A club statement confirming the news said: "Peterborough United Football Club can confirm that the club received a written transfer request from striker Lee Tomlin on Wednesday morning.
"The request has been rejected by the football club."
The 24-year-old rejected a new deal in the summer and has recently been linked with Scottish champions Celtic, newly-promoted Premier League side Crystal Palace and Championship clubs Huddersfield and Brighton.