Barca wrap up their season against already-relegated Eibar on Saturday with nothing to play for after one win in their last five games ended their La Liga title hopes.
However, president Joan Laporta has always said he is "convinced" Messi will renew, and sources have told ESPN that Barca plan to offer him a two-year deal with the option for an additional year.
The terms also will include the chance for him to finish his career in Major League Soccer before returning to Barca in a non-playing capacity.
Messi wanted to leave last summer, with Manchester City the leading candidate to sign him, but the club refused to let him go.
City and Paris Saint-Germain continue to monitor the forward's situation at Barca amid the possibility of signing him for free this summer.
Messi's transfer request came after the 8-2 defeat to Bayern Munich last season, but a large part of his desire to move on was rooted in a fallout with the previous president, Josep Maria Bartomeu, and his running of the club.
Bartomeu has since resigned and been replaced by Laporta, who was the president when Messi first broke into the Barca side and signed his first professional deals with the club.
Laporta has maintained that he is optimistic he can persuade Messi to stay, while Messi has said he will wait until the end of the season before deciding on his future.
Ronald Koeman's side are set to finish outside the La Liga top two for the first time since 2007-08. The Blaugrana were also knocked out of the Champions League in the round of 16 for the first time since 2006-07.
However, Koeman's side did win the Copa del Rey, and Messi played a key role in a 19-game unbeaten run midseason that helped Barca fight back from 13 points behind Atletico Madrid to get back into the title race before throwing it away over the past two weeks.
Laporta has said the manner in which Barca lost the league was "incomprehensible" and, speaking earlier this week, promised several changes as a "cycle comes to an end" at the club.
Messi played 47 games for Barca this season and scored 38 goals in all competitions. He will join up with Argentina in the coming weeks for the Copa America, where they kick off their campaign against Chile on June 13 in Buenos Aires.