After an initial offer of £1.5m was rejected last week, Celtic reportedly went back with a £1.75million offer, which was rejected as well.
Hibernian head coach Neil Lennon said: "We have rejected two bids from Celtic."
"Our club has a valuation of the player. I don't know what that is, but obviously Celtic have not met the valuation that Hibs want."
"Obviously it is difficult. Listen, I have been a player myself, so it's difficult dealing with speculation."
"Obviously when a club as big as Celtic come in for you there is always that anticipation, from his point of view, of maybe making that step forward, if you want to call it that."
"However, he has to be professional. We have had a couple of chats over the piece about it. He will just have to wait and see how it develops because he is our player, and he's a very important player for us."
McGinn has been capped nine times for Scotland and has only a year left on his contract with Hibs.
He has attracted quite a lot of interest, with Premier League clubs and Scottish giants Celtic all wanting to make a deal.
The 23-year-old joined the club from St Mirren in 2015, and has made 132 appearances since then, scoring 15 times and winning the Scottish Cup in 2016.