Spurs lost 2-1 to Southampton but thanks to their vastly superior goal difference need just one point from their final game at Newcastle United on Sunday to finish above Arsenal for the first time since 1995.
"It would be a really good feeling (to finish above Arsenal)," Kane, the league's leading scorer with 25 goals, told British media.
"It was not something we focused on at the start of the season but now we are here it would be good, it would be good for the fans."
Arsenal have mocked their north London rivals for years by celebrating St Totteringham's Day, the moment when Spurs can no longer overtake them in the league, and Kane disagreed with Wenger's assessment that Spurs finishing above his team would be a one-off.
"That's his (Wenger's) opinion, they are going to want to finish above us next season and we will be trying to finish above them. We want to finish as high up as we can, we are not going to focus on anything but ourselves," Kane added.
"Next season we will try and fight for the title again."
Arsenal host relegated Aston Villa in their final game on Sunday.
(Reporting by Nivedita Shankar in Bengaluru, editing by Ed Osmond)
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