The 21-year-old was voted PFA Division Two player of the year for 2012/13 after netting 41 times in a record-breaking campaign for the Doonhamers.
His fine form drew plenty of admiring glances from afar, with Ibrox boss Ally McCoist among those to have taken note of his efforts.
Clark has now held talks with the Gers and is hoping to see a summer move pushed through before the end of May.
He told the Evening Times: "I have met Ally already and we talked over his plans and it's exciting to be in them.
"I am hoping to meet him again at Ibrox next week and hopefully get the deal signed and realise my dream of becoming a Rangers player for the next few seasons.
"It is something I have always dreamed of and to have met Ally in the first instance was just really flattering, but it was hard to take in that he wanted me to come to the club I have supported all my life.
"I have had a great season at Queen of the South and, at 21, I never stopped hoping that maybe I had done enough to get on Ally's radar.
"To have actually spoken to him and heard his plans was massive, but it will only really sink in when I sign on the dotted line.
"I may have scored over 40 goals for Queens this season, but I believe I could score even more for Rangers with the quality of the players they have in the side.
"My ambition is to play in the SPL and to do it with Rangers one day would be as good as it gets."