"Kane turns 27 in July," Carragher wrote in his Telegraph column.
"We have no idea when the next transfer window will open or next season start. If Kane does not leave soon, the situation gets trickier for him.
"When players hit 28, psychologically it makes a big difference to clubs. They see him as nearer 30, recognise there is no resale value and balk at high valuations.
"Manchester United's need for a top-class No.9 is urgent and they might see Kane as the ideal fit, but they will apply the same logic if the fee is upwards of £150 million."
Carragher summarised that the forward had "reached the crossroads of his career at the worst time possible".
He continued: "In other circumstances, the Tottenham striker's comments suggesting he would consider a move in the near future would be reasonable.
"Spurs fans may not like it, but I can understand why Kane is wondering whether his trophy ambitions will be served elsewhere."