Former Celtic manager Neil Lennon is currently in charge at the Macron Stadium and previously spoke of his desire to recruit the Hoops favourite, who is in the final few months of his contract with the Parkhead club, as reported by the Daily Record.
Bolton are believed to have made a £250,000 bid for the playmaker back at the start of January and Express is now claiming that the Championship club are set to return with an improved offer for the star this week.
Commons is unlikely to sign a new deal at Celtic Park in the coming weeks, meaning the Glasgow club risk losing him for nothing in the summer.
According to the Express reports, the ex-Derby and Nottingham Forest man is only willing to stay at the club if a two-year contract extension is offered, with the Bhoys only able to table a one-year deal.
The only other option would be for Commons to depart the club for a nominal fee this January and Bolton’s coffers have been boosted by their weekend stalemate with Liverpool.
A 0-0 draw with the Reds at Anfield earned the Trotters a replay and some additional income prior to the close of the mid-season transfer market.
The 31-year-old has played 175 games for the Hoops to date, scoring 73 goals and was named the PFA Scotland Players’ Player of the Year for the 2013-14 campaign.