The Catalan giants were knocked out of the Champions League in the last-16 stage on Wednesday after a 1-1 draw with Paris Saint-Germain at the Parc des Princes.
That followed the Ligue 1 side's thumping 4-1 win in the first leg at Camp Nou last month and means Barca have failed to reach the quarter-finals of the competition for the first time since the 2006-07 season. Their run of 13 consecutive last-eight appearances was the longest in Champions League history.
Messi, who cancelled out Kylian Mbappe's opener with a stunning strike before missing a penalty, has been tipped to leave on a free transfer at the end of the season, with PSG and Premier League leaders Manchester City the reported frontrunners for the 33-year-old.