Kane won a much-anticipated maiden international call-up for Friday's Euro 2016 Group E qualifier against Lithuania and the subsequent friendly with Italy in Turin, having scored 29 goals during a stunning breakthrough season at club level.
Hodgson refused to confirm whether the 21-year-old would be in his starting line-up at Wembley next time out but praised how the player had trained with his new colleagues in the build-up.
"We are very happy with Harry Kane," he told a press conference.
"He has done well all week and has not in any way damaged his chances of playing in the full senior team.
"I'm pretty sure over the course of these two games he will make his full debut, but I'm not prepared to give my selection away and when that is people will have to wait and see."
Hodgson's words increase the chances of Kane being paired with Wayne Rooney during the forthcoming games and the England captain was full of praise for his form.
"The season Harry Kane has had is incredible," said the Manchester United forward.
"His first year in the Premier League, the goals he has scored and his performances mean he has deserved his call-up.
"He is a finisher, as we saw against Leicester [Kane scored a hat-trick in Tottenham's 4-3 win last weekend].
"It is great for English football to have someone performing like he is."
