Posh manager Darren Ferguson insists Tomlin is "100 per cent not leaving" despite the Glasgow giants stepping up their interest ahead of the Scottish transfer deadline.
Ferguson said: "I can confirm Celtic have made three bids on the day of a game - including one while our game was going on - and completely unsettled my player.
"If that is how a big club like them choose to do their business then so be it, I'm not going to criticise them for it.
"But Tomlin is not for sale so they can bid for him as much as they like. He is 100 per cent not leaving.
"We are trying to build something good here and we need to keep hold of our best players.
"Lee has clearly been ill-advised but I have to manage the situation and deal with it."
Ferguson refused to reveal the value of Celtic's bid for Tomlin.
The 24 year-old started for Posh in their 2-0 defeat to Crawley, but was substituted at half-time.
Tomlin, the scorer of six goals this season, had a transfer request rejected by Posh earlier this month.
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