Since Barcelona's embarrassing exit in the Champions League quarter-final against eventual tournament winners, Bayern, Messi's future at the club has been called into question.
New head coach Ronald Koeman and Messi reportedly spoke last week, but the Barca captain refused to commit his future to the club which naturally catalysed speculation that he could leave.
Inter, Man City, and PSG have been mentioned as potential destinations.
Tuchel was asked about a Messi arrival after having witnessed his side lose the Champions League final, replying that he would be open to the idea.
"He's very welcome. What coach says no to Messi?" the PSG boss told BT Sport when asked if he would be interested in signing the six-time Ballon d'Or winner.
Although it seems like a Messi transfer to PSG is unlikely, Tuchel did admit that the Ligue 1 champions need reinforcements in the transfer window if they are to compete for the Champions League again.
"We lost lots of players for this campaign and we lose now Thiago Silva and Eric Maxim Choupo-Moting," he added.
"We need to use the transfer window now to make the squad wider. The campaign will be very demanding without any breaks.
"We need to build a strong squad. We decided not to talk about transfers in this period. We'll sit together in the next days."
PSG lost the final in Lisbon after a solitary goal from former player, Kingsley Coman.