The 33-year-old has become more and more disgruntled with life at the club in recent times and his contract is set to expire next summer.
They believe a move to the club to reunite with his most successful manager at Barcelona would be enough to secure him ahead of other teams who might be interested.
Messi has been linked with a move away from Barca after clashes with the club’s hierarchy with Inter Milan recently expressing an interest.
After disappointments against Roma and Liverpool in the Champions League in the past two seasons, Messi had one of his worst nights in a Barcelona shirt as he was powerless to stop a relentless Bayern Munich smashing them out at the quarter-final stage once again.
A photo of the forward looking disconsolate at half-time emerged after the game, casting further doubts on his future – which had already been up in the air amid rumours he is unhappy with Quique Setien in charge.
The Argentine looked at the floor as goalkeeper Marc-Andre Ter Stegen stood by the door, also looking downcast before heading back out for the second half.
Despite his recent displeasure with the goings on at the club, Messi has yet to decide what his future will be and City will be one of several clubs keenly watching to see if he decides to commit his future to the club or not.
Speaking on BT Sport after the game, Ferdinand questioned whether the Argentine will be tempted to leave the Nou Camp with the club in disarray and without a major trophy.
‘What is Messi thinking going home?’ the pundit asked. ‘Does he want to spend his time left in that shirt given the performances and the way the squad is looking at the moment in comparison to other teams around Europe.
‘Has he got the time to sit there and wait?