Messi has been strongly linked with a move back to the Nou Camp next summer.
The seven-time Ballon d'Or winner is now into the final year of his current deal with French side Paris Saint-Germain, who are keen to tie him down to an extension.
Messi is free to speak to foreign clubs in January once he has entered the final six months of his contract with PSG, with speculation mounting that he could agree to rejoin Barcelona next season.
Messi was forced to leave Barcelona in 2021 after the Catalan club were unable to fulfil a contract that had been agreed with the Argentina international due to "financial and structural obstacles".
Barcelona's financial difficulties have continued since then, with the La Liga side forced to sell off significant assets this summer in order to fund transfers.
However, Romeu insists Barcelona are in a position to make Messi an attractive offer, should he wish to leave PSG at the end of the season.
"It would be possible financially because if he returned it would be as a free agent," Romeu said to El Mati de Catalunya Radio.
"But it's a decision which has to be made by the coaching staff and the player. It doesn't correspond to me [to make those decisions], but it would be viable. Although I don't have it in the budget."
"He is an icon of the club," Romeu added.
"This will always be his home, but it will be a technical decision [if he returns]."
Barcelona head coach Xavi has already admitted he would like Messi to return to the Nou Camp, where he won 10 La Liga titles and the Champions League four times.
When asked if he was keen to see his former teammate return to the club, Xavi said: "Yes, but at the moment, Leo has a contract with another club, so it's impossible."
But he added: "We will see in the future."
Messi, however, has indicated he could remain with PSG for another year.
He has already scored six goals and provided eight assists for the French champions this season, while he also scored four goals while on international duty with Argentina this month.
And the 35-year-old says he now feels settled in France after a difficult debut season.
"I feel good, I feel different from last year. I knew it was going to be like this," said Messi.
"I'm more comfortable with the club, the dressing room, my teammates, the game.
"I feel very good again, so I'm starting to enjoy it again."
Featured Image Credit: Alamy
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