It is four years since Barca last reached the semis of Europe's premier competition but a 1-0 victory at Old Trafford makes them firm favourites ahead of the return at Camp Nou.
Messi was among 10 players rested for the goalless draw against Huesca on Saturday after a hefty challenge from Chris Smalling last week left him with a swollen nose and cheek.
"He is fine," said Valverde at a press conference on Tuesday. "He has recovered perfectly from the blow he suffered. He was fine after a couple of days.
"It is true that during the match he was a little stunned but he is in perfect condition and does not have any problems ahead of tomorrow's game."
Valverde said Ousmane Dembele could also feature after he played for 67 minutes against Huesca, having recovered from a hamstring injury. "I don't know to what extent because he has been out for four weeks," Valverde said. "But he is ready to play."
Barcelona have lost only one home game in the Champions League in 10 years but United will take hope from their last 16 comeback against Paris Saint-Germain, when they overturned a 2-0 first-leg defeat to go through.
"That memory from PSG will help the players and us as a team, that we know we can turn things around," coach Ole Gunnar Solskjaer said.
"Barcelona here at the Nou Camp is a difficult prospect but the memory will live with the players, it's not long ago."
Barca goalkeeper Marc-Andre ter Stegen is confident his team can avoid a repeat. "The good thing is we play differently to PSG," he said. "But United are dangerous and the result from the first leg is dangerous, it is a very small advantage."
Ole Back to Barca
Solskjaer might also draw upon his own experience of the Camp Nou, in 1999, when he scored a 93rd-minute winner as United came from 1-0 down to beat Bayern Munich 2-1 in the Champions League final.
"Of course it's a fantastic memory for me. It's the only time I've been on the pitch here," Solskjaer said.
"I dont mind if we score in the 93rd minute. If we get to injury-time we are a fit team."
Barcelona's recent history in this competition has been more painful as United look to follow Juventus, Atletico Madrid and Roma in sending them out in the quarter-finals for a fourth year in a row.
"It has been hard," said Ter Stegen. "We are another year older and we want to make sure it doesn't happen again. We have to take those losses into account and use them to move forward."
Valverde urged his players to seize the opportunity. "I think we all take examples of things happening in the past and use them to spur us on," he said. "That's fine but I prefer to take charge of your own destiny. You won't be given something that falls from the sky. We have to earn it."
United's greatest threat in recent weeks has tended to come on the counter-attack but Solskjaer insists they cannot afford to sit back.
"There are freak results against Barcelona when you have 10 or 15 per cent possession and they don't win but normally they do win," Solskjaer said. "We need to stamp our authority on the game."