Since signing for the Saints, Minamimo has featured just nine times and has two goals to his name.
Hasenhuttl acknowledges that Minamino has settled in well at St Mary's, and says that he will have talks with Liverpool over what is next for the player.
"I must say. He was a very lively factor in our game, in the games he played," Hasenhuttl told Hampshire Live.
"He not only scored fantastic goals but his mentality and his character really fit into our team. You can see why a club like Liverpool wanted to sign him.
"He did a good job here. We gave him a chance to show up. We will have a look what happens in the summer, we will see what Liverpool want to do.
"There are discussions going on but we will have a look in the summer."
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