The Ligue 1 champions are one of few clubs in the world that could potentially afford a move for Messi and Tuchel conceded he certainly wouldn’t say no to having the 33-year-old to join his side.
“He [Messi] is very welcome! We lost lots of players for this campaign only and we lose now Thiago Silva and Eric Maxim Choupo-Moting. We need to use the transfer window now to make the squad bigger,” Tuchel told BT Sport.
“The campaign will be very demanding without any breaks. We need to build a strong, strong squad.
“We decided not to talk about transfers in this period here. We will sit together in the next days. We have many things to do to keep the level of the squad.
“What coach says no to Messi? I think Messi finishes his career in Barcelona. He is Mr. Barcelona.”
Despite a few chances to strike against Bayern, PSG were unable to triumph in their first Champions League final and Tuchel called on his men to rebound quickly next season.
“It is necessary if we want to keep the same level, we have to step up again. You have to go on. This level is necessary,” Tuchel said.
“We showed again we can compete with the best teams in Europe with this mentality and attitude, in combination with our talent.
“We are a strong, strong side. We can be proud of that. We cannot worry too much because it is okay and we will go on.”
While once again falling short on Europe’s biggest stage, PSG ended their season with a domestic treble and lost just three games in a shortened Ligue 1 campaign.