Messi was sentenced to 21 months jail for tax fraud but is not expected to do any time because prison terms of less than two years in Spain can be served under probation.
Barca immediately issued a statement supporting their player but Messi is known to feel that the club could have been more supportive during the case.
The fee for Messi would smash the £100million mark and SunSport understands that Messi’s father, who represents his superstar son, has met with Blues’ owner Roman Abramovich.
The meeting is believed to have taken place in the last ten days on Abramovich’s personal superyacht, the Eclipse.
Chelsea chiefs have been monitoring the tax fraud case which saw both Leo and his father convicted.
Between them, Messi and his dad have been ordered to pay just under £3million in fines and the family feel victimised by Spanish authorities.
The Stamford Bridge club were alerted to the possibility that Messi could leave Barca over the tax case and the club’s failure to offer a new contract.
Negotiations were initiated on the basis that if the 29-year-old decided he’d had enough then Chelsea would be in pole position to capitalise.