'In my opinion, Liverpool should say ''thank you very much for your service, we'll keep this professional, on you go'', Jenas told BBC Radio 5 live.
The midfielder, who is out of his team's Premier League opener at Watford due to a back injury, is keen on a move to the Camp Nou and sees it as his only chance to join the Catalan giants.
'The problem is, are Barcelona ever going to come back?', Jenas said. 'If they go out and find someone else, that chance has gone', he added.
Coutinho joined Liverpool from Inter in 2013 and feels the time has come to move on. Jenas continued: 'He'll be looking at this from a player's perspective going: ''This is my opportunity. I've given everything I can for Liverpool, this is my one chance to get to Barcelona and I'm going to do whatever it takes to get there''.
The former Spurs man concluded by suggesting that the relationship between the club and the player would be very much stifled: 'It is going to get messy. The player wants to leave. The club have given him almost nowhere to move', Jenas said.