Barcelona are expected to bid for Coutinho despite seeing Liverpool rebuff three offers back in the summer.
The Brazil international recently skippered the side in the 5-0 win over Swansea on December 27.
And Klopp, speaking as his team prepare to face Leicester, has joked that Coutinho will stay for life should he wear the armband on a regular basis.
“It was exactly how I said it,” he said.
“When Hendo and Milly aren’t playing, Coutinho is the longest-serving.
“Maybe I could be smarter and think if I give him the armband, he will never leave.
“That isn’t how it works but he did very well with it.
“You can feel the lift or the pressure and it didn’t affect him.
“It is a really good moment for him and he has played very well for the last few weeks.
“It is just an armband.”
Klopp also refused to rule out players leaving in the New Year.
“The first thing we must make sure is that we have the squad for the second half of the season,” he added.
“Players have longer contracts but everything can happen in the summer.
“We have to see what we do.
“The club’s interest comes first and we must make sure we have enough players for different situations.
“It has to be perfect for the player and the club – but if not, the club comes first.
“There is interest in our players but there has been nothing agreed so far.”