Messi, 33, is out of contract with Barca at the end of June and has previously expressed a desire to play in the United States in the final years of his career.
Barca president Joan Laporta is "convinced" Messi will extend his stay at Camp Nou in the short term, although the club are working on a long-term deal that would allow him to end his career in MLS.
Mas has confirmed that he and co-owner David Beckham are hopeful of accommodating the Argentina international in Miami if he does decide to move to the U.S.
"David and I have been working really hard, we have aspirations of bringing the best players here and Messi is a generational player, arguably the best player of all time," Mas told the Miami Herald.
"I am optimistic Messi will play in an Inter Miami shirt because I think it will complete the legacy of the greatest player in our generation and will meet with the ambitions of the owners of Inter Miami to build a world-class team."
Messi wanted to leave last summer but following the exit of previous president Josep Maria Bartomeu and the election of Laporta, sources at the club are bullish about the chances of him continuing his 20-year association with Barcelona.
ESPN revealed earlier this year that Laporta is working on a two-year deal with the option for an additional year.
Reports in the Catalan press have since suggested the full contract will be for 10 years, with Messi continuing in an ambassadorial role while ending his playing career in MLS after two or three more years at Barca.
Messi, who recently purchased a $7 million condo in Miami, would then return to Barca in a yet-to-be-defined behind-the-scenes role.
Messi's current terms are worth about $87m annually before bonuses, although Laporta has stressed that the attacker prioritises the club's sporting project and chances of success over any financial offer.
To put that into perspective, the highest-paid player in MLS is Los Angeles FC striker Carlos Vela, who is guaranteed to earn a minimum of $6.3 million each season.
Speaking last December, Messi confirmed his desire of playing in America.
"I always had the dream of being able to enjoy and have the experience of living in the United States and experiencing what the league there is like," he said.
Messi is currently with the Argentina national team preparing for the Copa America, with his dad, Jorge, taking charge of contract negotiations with Barca.
Manchester City and Paris Saint-Germain have both been monitoring the situation, but sources told ESPN at the end of May that talks with the Blaugrana are progressing satisfactorily.