Speculation over Messi's future is intensifying with each passing day as his contract expiration date draws closer, with a number of possible next destinations being mooted for the six-time Ballon d'Or winner.
Messi has even left the door open for a potential switch to the United States, and Higuain is excited by Inter Miami's reported links with a fellow Argentina international, but is not certain he will want to stop competing at the highest level in Europe.
What's been said?
"I see no reason why Lionel couldn't come here. If it would make him happy, we would welcome him with open arms.
"At some point, he will decide where he wants to play play and what is in his own best interests on a personal and sporting level, but in my opinion, he has the caliber to continue competing for the Champions League."
WHAT ARE MESSI'S OTHER OPTIONS?
All three clubs have been tipped to submit lucrative contract offers for the Argentine, while it has also been suggested that a return to boyhood club Newell's Old Boys could hold great appeal to him.
Barca successfully blocked the 33-year-old's exit last summer but as it stands, he will become a free agent at the end of June.
Messi has said he will wait until the end of the 2020-21 campaign before deciding on his next move, with it still possible he could extend his stay in Catalunya following Joan Laporta's re-election as club president.
How has Messi performed for Barca this season?
Messi's status as the best active player in the game hasn't changed this season despite constant talk of him coming towards the end of his 16-year spell at Camp Nou.
The Blaugrana captain has scored 27 goals in 36 games in all competitions to date, including two in a 4-1 Liga win against Huesca on Monday.
Messi has also provided 12 assists for his team-mates while helping Barca compete for a league and cup double in Spain.