The Norwich forward is aware that Lennon is reportedly one of four bosses the relegation-threatened Canaries are looking at with a view to replacing the departed Chris Hughton.
The Northern Irishman's managerial CV includes three successive top-flight titles, two Scottish Cups and a last-16 appearance in the Champions League.
However, so far a clean sweep has evaded the Parkhead manager and Snodgrass, wearing his Celtic hat, is hoping that will be addressed.
The 26-year-old Scotland forward said: "The Celtic lads have great things to say about him so if that is what he is wanting (work in England) then good luck to him.
"But (with) the manager in charge now, even though we are not getting results, we are playing well in certain spells.
"It will be interesting to see who does get the job. I'm sure Neil Adams will put his name in the hat and push his own claim.
"I will let the powers-that-be upstairs decide that.
"But I'm a Celtic fan so I would like to see him trying to do better in the Champions League (group) stage and try to get the treble."
While there is talk of Lennon moving south, Snodgrass has for a while been linked with a move to Celtic.
However, the Glaswegian, who started his career at Livingston before moving on to Leeds United, is putting everything on hold to try to rescue Norwich from the drop.
The Canaries were beaten 4-0 at Manchester United on Saturday and have now slipped into the Premier League relegation zone on goal difference following Sunderland's win on Sunday, with their last two fixtures away to Chelsea and at home to Arsenal.
Snodgrass said: "There is always going to be lots of talk. Celtic are a massive club but I have a job to do for Norwich and I will focus every bit of my effort trying to keep Norwich in the league.
"If the worst comes to the worst and you look back with any regret, or if you could have done more, then I won't be able to live with myself.
"We have had very tough games over the last few weeks and it doesn't get any easier with Chelsea and Arsenal coming up.
"But I am relishing the challenge and hopefully we can do it.
"You must be doing something right if you are being linked with a club like Celtic.
"But I have another year left at Norwich and I will give everything I have got in my body for that club because they have been terrific with me.
"They gave me my chance to play in the Premier League so I will honour that."