Former Wasps director of rugby Gatland combined with current Wasps coach Shaun Edwards to lead Wales to an unexpected Grand Slam at the Six Nations, while McGeechan, who succeeded Gatland at Wasps in 2005, has been involved with six Lions tours - two as a player and four as a coach - including the last successful series in South Africa in 1997.
Hastings said: "You've got to think it sounds quite nice and sexy.
"It would be a very good team - I think that could work very well."
Hastings, in Hong Kong as an ambassador for HSBC, the sponsors of the 2009 Lions tour, added: "I'd be surprised if any of them aren't interested in doing it.
"Ian McGeechan is a Lions legend and all three of them have the ability to bring the best out of people and that's a wonderful talent to have, especially when coaching the Lions when you have to harness a team in such a short period of time."
Gareth Edwards concurred. He said: "They could present themselves with a great team.
"Ian McGeechan has been a very successful Lions coach so he knows absolutely what is required.
"But Gatland might very well prefer to be the number one."
The former Wales and Lions scrum-half, however, sounded a precautionary note, citing the example of former Wales coach Graham Henry, who led the Lions in Australia in 2001.
"Gatland might not be available," added Gareth Edwards, who played on three Lions tours.
"The Welsh Rugby Union had their fingers burnt when Graham Henry went with the British Lions - it didn't properly work as it's a huge commitment.
"And (former Ireland coach) Eddie O'Sullivan was odds-on favourite last year - a lot can change in 12 months."
Former Scotland full-back Hastings led the Lions on the 1993 tour of New Zealand and made six Test appearances.
The 46-year-old is adamant there is still a place for the spectacle despite the ever-growing rugby calendar.
"As long as there is due deference paid to the history and tradition of the Lions then I think there will always be a place - it is very special and unique," added Hastings.
"The prestige of being a Lion, because of the history and the tradition that has gone before, is so meaningful.
"You just need to reel off Gareth Edwards, Willie John-McBride, JJ Williams; more modern heroes in Jeremy Guscott, Martin Johnson and Matt Dawson; really talented players that were in winning Lions' sides."
Gareth Edwards believes many of Gatland's victorious Welsh squad will be on the plane to South Africa, if they can maintain their form.
"Wales would have a big say in the team on this year's performance," he added. "But maybe last year, you'd only have picked half a dozen.
"But in my experience, the Lions tour was influenced by the champion nation of that time."