Villa in the Championship in England have signed McGinn from Scottish Premiership side Hibernian in the summer transfer window.
According to The Times, the Villans paid Hibs an initial transfer fee of £2.75 million for the services of the 23-year-old Scotland international midfielder.
Former Celtic and Scotland international striker Burchill has revealed that he heard that McGinn wanted to move to Celtic.
The 37-year-old has also said that the Hoops have missed out on a good player in McGinn.
Burchill told The Scottish Sun: “At the end of the day, I think that Celtic probably felt that they had a ceiling price to pay.
“And that price wasn’t obviously accepted by Hibs. It’s a great move for John to go down to England.
“By all accounts I heard that he wanted to go to Celtic. But as a player you can only go to the team that the club agree a deal with so Celtic have missed out.
“He’s playing every game for Scotland in midfield and Celtic have missed out on a good player.”
According to The Scottish Sun, Celtic had as many as three bids for McGinn turned down by Hibernian.
Manager Brendan Rodgers’s reportedly wanted the midfielder, but it seems that the Celtic board did not meet the transfer fee demands of Hibs.
McGinn would have been a great signing for Celtic, not just for now but in the long run, as the midfielder is only 23 years of age.