The six-time world player of the year is a free agent after Barcelona announced they were unable to fulfil the terms of a new contract due to financial difficulties.
The 34-year-old bade an emotional farewell to the Catalan club at a press conference at the weekend.
PSG were immediately linked with the Argentinian and it is now being claimed Messi is set to sign a two-year deal with the French club.
The move would see him link up with his former Nou Camp team-mate and Brazil star Neymar. Messi has reportedly remained in Barcelona since the weekend but will now travel to the French capital to finalise the switch.
Messi has played his entire club career to date at Barca after joining the club at the age of 13.
He came close to leaving the club after a disagreement last summer but that was eventually resolved. His contract expired at the end of last season and he had agreed to take a pay-cut in a new deal but the club were still unable to proceed.
He leaves Barca as their record goalscorer with 682 and having won 35 trophies.
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