The Irish striker is not interested in a move away from St Mary's at this point in time.
The report claims that both Jurgen Klopp and Mauricio Pochettino are fans of the Republic of Ireland international who has two-and-a-half years left on his deal at St Mary's.
He is quoted as telling the Irish Sun this weekend:
"I'm here to stay.
"There's good competition in the squad. That pushes every player to play to their best because someone is waiting to jump in and take your spot.
Long is certainly something of a Marmite player. His work rate and pace are often let down by his composure and finishing but he has caught the eye in recent games for Ireland v Germany and Southampton v Arsenal.
But right now it seems he is focused on keeping a place in the Southampton first-team after the arrival of Charlie Austin from QPR this week.