The former Burnley defender has hit a form slump in recent weeks.
But Stubbs has been thrilled by what he has witnessed already.
“He (Keane) is the future of Everton in that back line," he said.
"I think he was a great signing."
Meanwhile, Everton chief Steve Walsh had a scout posted at Wembley on Friday night.
RB Leipzig left back Marcel Halstenberg was the subject of Everton's interest.
Halstenberg, 26, has been a key player for Leipzig ever since signing from St. Pauli in 2015. He made his Germany debut against England.
Halstenberg has attacking quality, crosses well from set pieces and is strong defensively.