Messi is part of the squad that travelled to Milan for the European duel, and Valverde told the media on Monday that the Argentinian "might be available" a little more than two weeks after fracturing the radial bone in his right arm:
"Leo is at the point where he might be available, but we have to wait for the training session. We have to see if he's safe to play.
"In terms of his play and his movements, he's fine. We have to wait. ... It's always better if he's there. Of course it's necessary to get Messi back as soon as possible.
"There are three or four possibilities. One is that he plays from the start, or he comes on, or he goes off. What we won't do is take any risks."
Barcelona triumphed 2-0 in the first group meeting between these two teams, when Rafinha and Jordi Alba supplied the goal in the absence of their South American star.
Inter manager Luciano Spalletti was honest in his assessment of the five-time Ballon d'Or winner ahead of Tuesday's decision, via Goal:
The Blaugrana lead Inter by three points in Group B, while Tottenham Hotspur and PSV Eindhoven are hoping to claw their way back into contention, each five points off second with a point each to their names.
Barca already proved they can beat the Nerazzurri without their most valuable star ahead of what looks to be the toughest fixture left on their group-stage schedule.
However, Valverde may be tempted to give Messi some playing time at the San Siro considering his side can secure top spot in the pool with two games remaining should they emerge as victors.
All three of Messi's previous career meetings against Inter came during the 2009-10 season, per Transfermarkt, but he's failed to find the back of the Nerazzurri net so far.
That's a drought he'll be keen on ending should he feature in Italy.
Messi also holds a balanced record of one win, one draw and one defeat against Inter across those three matchups, with the Milan giants having gone on to win the Champions League under Jose Mourinho in 2010.