"It depends if I’m playing but I’d definitely be open now to having my family out here, so let’s just hope we win on Thursday and then we beat whoever we play in the next round and we’ll see," he said on Tuesday.
England play Belgium on Thursday in their final Group G game but have already qualified for the knockout stage with their opening two victories.
There have been no reported racist abuse from fans at England games and Rose said his experience in the country had been positive.
"It’s the first time I’ve been in Russia, and it’s different to what I expected. I’m having a great time," he said.
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"Our hotel is a bit out of the way, but it’s been really quiet. The weather’s amazing. I haven’t had much time to go out into St Petersburg yet but from what everyone says, it’s beautiful.
"They’ve (his team mates) had a look at the museums. There’s a beach just around the corner from us. The further we go in the competition, I’ll look to go out and see much more," he added.
Rose was on the bench for England's wins against Tunisia and Panama but could be one of those who get a chance to feature in the Belgium game.
The Tottenham wing back said he had missed his relatives during the team's family days.
"We’ve had family days where we’ve had a day off and the gaffer has allowed people, families to come to the hotel or we can go to our families’ hotel, When people have had their families around, yeah, it has been difficult," he said.
(Reporting by Simon Evans, editing by Pritha Sarkar)
