The 23-year-old Scottish midfielder, who has just a year left on his current contract with Hibernian, joined the club in 2015 from St Mirren.
Meanwhile, the Hibs have already rejected another want away midfielder Dylan McGeouch, whose intention is to join Sunderland after his deal expires.
However, Celtice are ready to include Scott Allan, who just returned from a season long loan from Leith in the deal to sign Mcginn.
The Scotland International 23, who was signed by former Hibernian manager Alan Stubbs, when they were fighting to gain promotion back to the Scottish Championship in two consecutive years.
Nevertheless, their dream of regaining promotion were quashed again in 2015/2016 season, but they ended their clubs search of lifting the Scottish Cup over a Century by winning it that same season with McGinn an important member of the record breaking Hibs team, he was also called to the National team, where he made his first International appearance same campaign year.
Due to McGinn prolific display throughout the season, he was named PFA Scotland’s Championship Player of the year award, and the following season Hibs won the second-tier league that gained them promotion to the Scottish Championship under Lennon.
There performance last season earned them a fourth place finish with a total of 67 points with the help of the two midfielders McGeouch and Allan McGinn.
John McGinn has netted 15 goals in 130 appearnaces for the Hibs and has earned 9 caps for his National team.
Although, there is a sell-on clause in John McGinn contract which will allow his previous club St Mirren to earn a certain compensation if being sold by Hibernian.
Another Mirren player Allan, 26, who joined the Hibs in 2014 and won PFA Scotland’s Championship Player of the year on the process.
He made just 17 appearances for Celtic when he joined them in 2015 through Ex-Celtic manager and then the new Scottish manager Brendan Rodgers.
The 26-year-old Allan had a wonderful outing with Hibs after returning from double loan deal with Rotherham United and Dundee with his prolific goal against the Herats, he scored a total 3 goals in 15 outing.
It’s yet to be seen if Hibernian will accept the offer for the midfielder from the reigning Scottish Champions.