Clark has caught the eye of Gers manager McCoist after netting 40 goals for the Second Division champions this season.
McCoist has already held talks with the player's agent and his father Sandy a former Gers player, who is the Queen of the South assistant.
He hopes to meet the 21-year-old in the next few days, but a transfer embargo means the club must wait until September 1 to sign free agents and January 2014 before buying new players.
He said: "I've spoken to Nicky's agent and I've spoken to his father, who I know reasonably well, just to let them know that we have an interest in talking to Nicky and meeting up with him and seeing if there is a possibility of him coming to the club.
"We are no further down the line than that, but I spoke to Sandy and I'm very keen to meet up, as are Sandy and Nicky, so hopefully we can get a meeting in the next couple of days.
"His goalscoring record is fantastic and we certainly need strengthening in forward areas, as we do all over the park."
McCoist is targeting a number of out-of-contract players and has handed a trial to Argentinian defender Cristian Trombetta after the 26-year-old left Mexican side Jaguares de Chiapas.
"He's been in for two or three days training. He's having a look at the place and we are having a look at him," said McCoist.
"There is nothing concrete yet but it goes without saying that we are desperately trying to bring players in to the club for next season."