The Paisley men won 2-0 in their fourth-round tie against Irn-Bru Second Division side Brechin City with something to spare at the weekend, despite the fact that top scorer Thommo had to sit the tie out with a rib muscle injury.
Ironically, with St Johnstone the visitors to Greenhill Road this Saturday, Danny Lennon's men will have the chance to land an early psychological blow and Thompson is hopeful he will be fit to return for the meeting of the Saints.
The seven-goal striker said: "At this stage in the competition any home draw is a good one. You would probably have to say that St Johnstone are favourites to make it through to the fifth round, even though they have to go to Central Park next Monday and get the win.
"No disrespect to Cowdenbeath whatever, but I would think St Johnstone will have too much firepower for them and, if they do prevail, then we will welcome them to Greenhill Road.
"They beat us up at McDiarmid Park back at the beginning of October when we were a bit slow getting out the blocks. But our record against them isn't too bad and, if you get home advantage at this stage of the tournament, you must make the most of it."
Although frustrated with the rib injury that kept him out of Saturday's fourth-round canter over the Glebe Park men, Thommo saluted the job done by his team-mates in his absence.
The Saints star said: "I thought there were a number of big performances from our boys but, in particular, Kenny McLean and Gary Teale impressed me.
"It was interesting to watch the game from the stand and I felt we were very comfortable, but it would have been good if we could have added another couple of goals.
"Brechin came into the tie on the back of an unbeaten seven-game run and we did our job well to take our own run to three unbeaten."
Regarding his own prospects of returning to the fray, Thommo said: "The injury has improved over the last few days and I am hoping to get back in training over the next day or so."
Full draw: Raith Rov v Celtic or Arbroath, St Mirren v Cowdenbeath or St Johnstone, Dunfermline v Dumbarton or Hamilton, Hibs v Aberdeen or Motherwell, Falkirk v Forfar, Dundee United v Rangers, Dundee v Turriff or Morton, Kilmarnock v Inverness or Ross County. Ties on weekend of February 2 and 3.