Jones, 18, was "outstanding" for the Under-21s this month and has also excelled in central midfield for Rovers in the last two games against Manchester City and Fulham.
Allardyce said: "It has been a great start to the season for Phil, carrying on where he left off last season and it's extremely exciting for him and for us.
"We're having to keep a close eye on him to make sure he doesn't slip away in terms of getting carried away with the attention.
"He's not just been good for us - apparently he also had two outstanding games for the England Under-21s.
"He has also been outstanding for us in midfield - against Manchester City, against players they had paid many millions for and though it was not his normal position, he looked very comfortable."