Messi requested to terminate his Barcelona contract in the offseason but, following a 10-day standoff, withdrew his request to avoid a legal battle with the club.
However, Messi's paperwork expires at the end of June, allowing him to join another club on a free transfer.
"Economically speaking, I would've sold Messi in the summer window," Tusquets told RAC1 radio station, as reported by Reuters.
"Both in terms of what you save on the wage bill as well as the money you make, it would've been desirable. But this is something the coaching staff have to consent to and that's not my place.
"La Liga are setting salary limits at the moment and this would've helped on that front."
Financial difficulties currently plague Barcelona. In November, the Catalonians were able to reach a principle agreement with players and technical staff over wage cuts that will save the club €122 million this season. The club had reported losses of €97 million over the 2019-20 term.
Meanwhile, Messi - the best-paid footballer on earth - is expected to bring in $92 million over the 2020-21 campaign, according to Forbes magazine. The 33-year-old has scored seven goals and assisted twice over 12 appearances this campaign.