With six months left on his current deal, Messi could leave FC Barcelona a free transfer at the end of the season if he fails to sign a new deal.
With PSG and Manchester City are reportedly the most likely destinations for the six-time Ballon d'Or, Pochettino claims all great players are welcome at the club.
"We leave the rumours aside. All great players are welcome at PSG," he said at his unveiling, as per Goal.
'Father Christmas has been generous with me, I take this opportunity to thank president Nasser [Al-Khelaifi] and [sporting director] Leonardo for the trust and to be in this great club and back in this house.
'It's one of the biggest clubs, if not the biggest in the world, so it's normal that there are rumours. We have just arrived so we leave them aside."