Messi, who joined Barcelona aged 13, has scored a record 634 goals for the club in 730 games and is also their most decorated player with 33 trophies but the 33-year-old is into the final year of his contract at the club.
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Reports in the Spanish media have cast doubts about his future at the club after a disappointing season that culminated in an 8-2 Champions League humiliation by Bayern Munich in the quarterfinals this month.
"He's very welcome. What coach says no to Messi?" Tuchel told BT Sport after his side lost 1-0 to Bayern in the Champions League final on Sunday.
"I think Messi finishes his career in Barcelona. He's Mr Barcelona."
Tuchel said the club would talk over their potential signing targets and that they needed a deeper squad to cope with the demands of the new season.
"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."
The 2019-20 French Ligue 1 season was cancelled in March amid the COVID-19 pandemic and the new campaign kicked off over the weekend.