The Sunderland star is the No.1 target to replace the Colombian who is in the final year of his contract.
They will then look to prise Stewart away from Sunderland following his 26-goal season as he helped fire the Black Cats into the Championship.
It is reported that Morelos is on a contract worth more than £30,000-a-week, which suggests Rangers would be able to offer Stewart a significant pay increase.
Sunderland will offer their star striker a new deal having signed him from Ross County.
Stewart is now a Scotland international after impressing manager Steve Clarke, making his debut in the win over Armenia last week and then a second appearance in the loss to Ireland on Saturday.
Clarke said: “He had quite a quick rise when he did well at Ross County, scored a few goals and got his move to Sunderland. I like the way he moves on the pitch and I like the way he scores goals.
“People might say, ‘He’s only scoring at League One level’, but you have to realise he is playing for a big club with big demands. Sunderland are definitely in the wrong league and there is always pressure at a club like that. But he’s produced the goods with the goals.”