Clearly a striker is high on the agenda for Lennon and it is somewhere we have struggled a bit this season, with Paul McQuade and Craig Dargo being injured for a fair mount of time.
It we could somehow lure Griffiths to Paisley he would be a terrific signing. He's scored 10 goals so far this season, 19 the season before and the same the year before that for Livingston. Dundee signed him from Livvy in 2009 in a bid to sell him on for a profit at some point in the future. However, their financial difficulties mean they could be willing to do a deal.
Even so it's unlikely we could afford him. He is a terrific talent and is highly rated for the future. Even if we can afford what Dundee want for him, chances are other clubs - including those in the Championship - would come in for him.
Despite that, Lennon said: "I'd face competition from the Championship for him as well but we're making progress. I'm delighted with how it's going."
Thompson has been linked with Saints in every transfer window since we were promoted. The former Cardiff, Rangers and Dundee United striker is a Saints fan, which is why the rumours have persisted. However, there has never been any concrete interest until now.
Lennon said at the recent AGM he had been in touch with Burnley and Thompson's agent about a possible transfer. The only problem now is Burnley are looking for a new manager and whoever comes in may want to keep him.
Lennon said: "I was keen on Stevie Thompson, but Burnley are now managerless and the goalposts could have moved. He is on good money down there, so he could have been out of our reach.
"He only has six months of his contract left. He is on a very good contract there, so whether we came to an agreement or whether it was a loan deal, we would pay as much as we could.
"I have spoken to his agent, so we will wait and see. He might see it as a new challenge for him if a new manager comes in. Depending who that manager is, he might love Stevie Thompson to bits. His family are up here and I think he is a St. Mirren fan, although I have not seen him at any games."
Landing either Griffiths or Thompson would require a sizeable outlay in wages or a transfer fee (or both), but Lennon seems to hint he does have money to play with - using a bizarre analogy.
He explained: "People talk about big budgets but while you can go to Marks and Spencer you can also go to Tesco. The cream of the talent will always be over-priced but that's just the way of it.
"We're currently working well within our budget so if we're going to do anything it's going to have to be from Marks and Spencer to get someone who can come in and make a difference to us."I'm confident that can be done."
Er, right. Anyway, it looks like this could be an exciting January and we are also being linked with some unnamed Queen of the South players - probably Paul Burns and Bob Harris.
Story sources: The Daily Record, The Herald