Messi has endured a disappointing season at Paris Saint-Germain although Barca's dire financial situation would make re-signing the Argentinian difficult.
La Liga's latest spending restrictions published last week set Barcelona's limit at -144 million euros ($159 million). It means the club will have to make considerable savings to sign anyone in the next transfer window.
Messi was let go last year because Barca could not afford to renew his contract, bringing an emotional end to the striker's historic career at Camp Nou.
Asked if he would open the door to Messi coming back, Xavi said: "He is the best player in history and the history of the club, he's earned the right to have the doors open to him.
"As long as I am coach the doors are open to him if he wants to come any day. He is the best in history and as a club we owe him a great tribute, he deserves it, but he has a contract with PSG, so there is little more I can tell you.
"If he wants to come any day, to see training, talk to the coach, the doors are open because he is the best player in the history of the club."
Without Messi, Barcelona struggled for much of the season but Xavi, who was appointed in November, has overseen a significant upturn in form.
