United are favourites for his signature, and he is hoping to secure a deal for next season in the near future.
Byrne said: "My contract will not be renewed at Sunderland which is disappointing but there is no hard feelings.
"There are a few things happening regarding me moving on and hopefully it'll be sorted soon."
Before he leaves the Black Cats he will be involved with the Ireland U21 squad as they face European Championship qualifiers against Germany, Switzerland and Russia.
He added:"We're off the pace but two wins would be a great finish to the season. There's also a game against Germany to look forward to."