Tusquets, who is in charge of the managing committee running Barca until a new president is elected on Jan. 24, said this week that it would have been "desirable" to release Messi from a financial point of view.
Sources have told ESPN that the comments didn't go down well at the club. Other managing committee members were surprised by what he said and feel he has made a habit of speaking too much since being handed his role in October.
"We know Leo's situation," Koeman said in a news conference in reference to the fact Messi is out of contract in June and free to speak to other clubs from January.
"But if there is someone that can decide their own future, it's Leo. Comments from outside the club are of no interest to me. But the comments inside the club don't help keep the peace of mind that we need to win matches. We can't control what others say. Inside it's different.
"It may well be [Tusquets'] personal opinion, and I respect all opinions, but Leo has another year at Barca. He will decide where his future will be. Hopefully it will be here, but he decides."
Messi's future has been uncertain since he told the club he wanted to leave in August following the 8-2 defeat to Bayern Munich in the Champions League.
Since then, Manchester City have been the favourites to sign him, although Paris Saint-Germain emerged as another potential destination after Neymar told ESPN he wants to play with Messi again next season.
"I think as a club always should try to have the best players here," Koeman said when asked if that could mean a Messi and Neymar reunion at Camp Nou -- the Brazil international spent four years in Catalonia before signing for PSG in 2017.
"I don't like to speak in terms of individuals, but as a club, as a player, as a coach, as a fan, you want the best players."
The Blaugrana have won their last three games in all competitions, scoring 11 without conceding a goal, and Koeman has set his players the challenge of winning all six league games remaining in 2020 as they look to bounce back from their worst start to a domestic campaign since 1991.
"We cannot afford to drop any more points," he added. "Between now and the end of the year, we have to win all our matches."