The England skipper is desperate to win trophies and hinted he could leave Spurs if they weren't matching his ambitions.
But Townsend, who played at Spurs with Kane, thinks Mourinho's trophy record would have filled the 26-year-old with confidence.
He told talkSPORT: "If Spurs had gone for another project - if they'd got maybe the Ajax manager [Erik ten Hag] in I would say he has to leave; he can't be waiting four or five years to get back to the top and win a trophy.
"But I am certain Jose Mourinho will win a trophy during his time at Spurs, whether that's the League Cup, the FA Cup or the Premier League and the Champions League.
"I feel with the manager they have, they can fulfil Harry Kane's ambitions, and I hope they do."