Brown, the Scotland hooker, missed the Six Nations with a neck injury but returned to club action last month.
The Lions are due to name their squad on May 6 for the tour of South Africa which means there will be only one round of Rainbow Cup fixtures before Warren Gatland’s announcement.
Wilson, the Glasgow coach, has backed Brown for a call-up and believes there are likely to be other Warriors players in the mix for the three-Test series against the world champion Springboks.
The Rainbow Cup features teams from the Guinness Pro14 and the four South African rugby franchises but has been plagued by doubts over whether the Stormers, the Sharks, the Bulls and the Lions will be able to play in the UK and Ireland due to Covid-related travel restrictions
Glasgow are due to play Benetton in Treviso a week on Saturday in their opening match. They will then play back-to-back derbies against Edinburgh but the inter-city games will take place after Gatland names his Lions squad.
Asked if he thought the Rainbow Cup was of sufficiently high quality for the likes of Brown to play his way into Lions consideration, Wilson said: “Yes, I do. I think that the derbies are the nearest things to international intensity. Everyone’s fired up to play in them and there’s a [1872 Cup] decider so you’re guaranteed that both teams will pick their full-strength sides for that game.
“There are some good sides in there.
“If we do get to play any of the South African sides…. They’re huge sides with quality, quality rugby players and they will be good tests and exactly the tests the likes of Fraser will want to play in to give himself any opportunity to put his hand up.”
Wilson believes other Glasgow players could be in the frame for a Lions call-up after Scotland’s impressive Six Nations campaign which included rare away wins over England and France and a record home victory against Italy. Glasgow forwards Zander Fagerson and Scott Cummings were particularly impressive and are likely to be on the radar of head coach Gatland.
The addition of Scotland coaches Gregor Townsend and Steve Tandy to the Lions backroom team will help strengthen the case for greater Scottish inclusion which Wilson believes would be merited.
“I’m hoping beating England and France away in the Six Nations and being competitive will give Warren Gatland the faith in some of those Scottish players who we know have been playing well and deserve an opportunity,” said the Glasgow coach.
“I’m hopeful that a whole host of them - maybe more than in the past - will get selected but we’ll have to wait and see.
“I certainly think there are a few boys here who put their hand up during the Six Nations and have played a fair amount of rugby and I’m hoping to see some good news from that point of view.
“And there’s two Scottish selectors in there now!”
Wilson confirmed that Glasgow’s first Rainbow Cup match against Edinburgh at Scotstoun on May 7 would decide the winners of the 1872 Cup.