Rofe was put in temporary charge of the the Cherries earlier this week after boss Paul Groves was sacked.
The former Leicester City and Chelsea defender lost his first game in charge on Saturday as Bournemouth were beaten 1-0 at Coventry City.
Rofe told reporters following the defeat that he is focused solely on helping the first-team squad at this stage.
He said: "That's never entered my head.
"I was asked to take the team and that's what I've done and the powers that be, above me, will decide what happens in the future."
Bournemouth are currently languishing in the League One relegation zone and are without a home win so far this season.