With Marco Silva's side strengthening in the summer, many are predicting them to push for a top six finish.
And Southgate believes that if Keane is at the heart of such success, it will only improve his chances of being a regular with England.
Keane was excellent for the Blues last season and it earned him a recall to the England squad for their Euro 2020 qualifiers against Bulgaria and Kosovo.
"It is going to be interesting to watch Michael with Everton [this season]," England boss Southgate told evertonfc.com.
"I think they are a very interesting team this year in terms of where they might finish in the league.
"We will have to assess in those bigger matches [resulting from being towards the top of the division] how he copes under intense scrutiny – and against those teams which cause you problems with their movement and pose different questions from the ones we might see here [in qualifying matches]."