Page is considered a future first-team left-back at the Hammers, but is finding his opportunities limited by Cresswell.
The Newcastle United midfielder has struggled for fitness and subsequently for form.
The Gers defender says the high standard and demands at Ibrox will stand him and the club in good stead this season.
West Bromwich Albion signed Queens Park Rangers winger Matt Phillips earlier today.
The Celtic man wants to hurt Mark Warburton's Glasgow Rangers, and hopes the Ibrox side are around long enough to do that.
West Ham United are expected to invest heavily in their squad for the upcoming season.
Tottenham Hotspur are reportedly keen on Newcastle ace Georginio Wijnaldum.
Henrikh Mkhitaryan has sealed his move to Manchester United.
The defender has had to look on as his country surprise many by reaching the semi-final of the competition.
The 33-year-old arrived at Goodison Park earlier in the summer and is already eyeing up a regular place in the first-team.