The Whites have been linked with the highly rated Liverpool youngster as they prepare for life back in the Championship.
Several other clubs have been credited with an interest in the 22-year-old, who spent the last couple of seasons in the Scottish Premiership.
“If I’m around, I’ll be looking to get on that pre-season tour (at Liverpool), hopefully get some minutes and impress,” Stephenson told The Athletic.
“I’m at the age now where I need to be playing first-team football, like I have done for the past couple of seasons.
“If that’s at Liverpool, fantastic. If it’s not, I’ll find a new adventure, like the other boys who have left and done really well.”
Stephenson grew up playing in midfield but has since found success at right-back or in a more advanced wing-back role.
When asked where he sees his future in terms of positions, the youngster replied: “It is right-back, or right wing-back. I’ve played under a few different managers now and they’ve always seemed to like me there.”
Stephenson’s first taste of EFL football came at Barrow before heading to Dundee United, where he made a positive impression.
The versatile full-back played 34 times during his first campaign in Scotland, which was cut short by injury. Despite that setback, he was named Player of the Year by both the club and its fanbase.
Stephenson returned to Tannadice Park last summer to continue his development under Jim Goodwin, chipping in with five goals and five assists in 29 starts. He even wore the captain’s armband at times.
“The best thing about Scotland is the range of games,” he explained. “It gives you Celtic and Rangers - and Hearts this year - playing in front of packed crowds at big stadiums.
“Then the derby against Dundee and how much it means to people. Then you have to go somewhere like Ross County midweek, again a different experience.
“I’ve felt really at home, and it’s a credit to the environment the manager and his staff have created. Trust, in football, is massive. The manager gave me that straightaway.
“That real trust can be rare, from knowing other young lads and their experiences on loan. I feel I can try things and the manager won’t judge you or have a go at you for it.”
Stephenson continued: “(Captaining the side) was a really proud moment. It showed where I am in my career and how far I’ve come.
“It’s a role that, in the next few years, I definitely want to take on, being a captain somewhere full-time.”