Lallana's current contract is set to expire at the end of June and Adkins wants to see him playing regularly again elsewhere.
"He's one of my favourite players," Adkins told Sky Sports News.
"So enthusiastic, so infectious, a very, very skilful talented young man who's a joy to work with every day.
"He's a talented player and it's important that he's playing.
"He's been out of the squad a lot, he's only a fringe player at Liverpool now which is a shame.
"It's a short career and you need to play, you need to go and play.
"So it doesn't matter where he goes for me, as long as you see him playing football, because he entertains you, he's exciting to watch, he moves to the left and moves to the right.
"He's a good player and he's a smashing young man with all the right morals and right values in life.
"I really like him and I'd love to just see him playing regularly again."