Giovanni van Bronckhorst's side ran out 2-1 winners against Blackpool in their most recent exhibition game, while the Hammers were held to a 1-1 draw by Reading.
Match preview
After a friendly with Sunderland in Portugal was comically abandoned midway through the game due to a floodlight failure, Rangers made the journey to Bloomfield Road and proceeded to survive a late scare to get the better of Blackpool 2-1.
Borna Barisic and Charlie McCann both struck in the second half for the Scottish giants before Beryly Lubala made things interesting with just one minute to go, but the Gers held on to make it two for two during a pre-season of paramount importance.
Still reeling from the disappointment of ceding the Scottish Premiership title to Celtic and the manner in which they lost the Europa League final to Eintracht Frankfurt, Rangers now return to their Glasgow base to face two English capital counterparts in West Ham and Tottenham Hotspur in the coming weeks.
Rangers have also put three past Partick Thistle in a 3-2 friendly win at their training ground this summer, but Van Bronckhorst will be itching for a clean sheet and made his feelings on Lubala's late strike for Blackpool clear after Saturday's triumph.
Prior to a trip to the Madejski Stadium, West Ham had already been pegged back by one lower-league side to draw 1-1 at Boreham Wood, and lightning struck twice for David Moyes's side in Berkshire on Saturday.
Nikola Vlasic drew first blood for the Hammers with 51 minutes on the clock, but Yakou Meite drew the Royals level not long after to ensure a share of the spoils and extend West Ham's unbeaten pre-season streak to four matches.
Moyes - who has also witnessed his Hammers outfit get the better of Servette and Ipswich Town in the summer months - was pleased to welcome back the majority of his international crop as preparations ramp up for another campaign of domestic and continental football.
After the showdown with Rangers, West Ham will round off their pre-season period away to Luton Town and Lens before the 2022-23 Premier League campaign commences, with the Hammers being assigned one of the most difficult early tests at home to Manchester City.
Rangers and West Ham are yet to lock horns competitively in any competition, but one can anticipate that will change soon as the two sides continue their quests for continental success.
Rangers pre-season form:
West Ham United pre-season form:
Team News
Rangers' new signings have been integrated into the squad by Van Bronckhorst straight away, with Rabbi Matondo, Tom Lawrence and John Souttar all coming off the bench against Blackpool.
The Gers have also sealed a loan deal for Bayern Munich starlet Malik Tillman, who could make his debut here, but Calvin Bassey was not involved at the weekend as he closes in on a move to Ajax.
Ianis Hagi is making progress in his recovery from a severe knee injury but will still be out for some months, and he is joined in the treatment room by Kemar Roofe, Filip Helander and Alfredo Morelos.
As for West Ham, Craig Dawson and Tomas Soucek were both absent from the draw with Reading due to minor injury problems, and it remains to be seen if the duo will be risked on Tuesday.
Angelo Ogbonna got some more minutes in his legs after his comeback from knee surgery, while Declan Rice, Jarrod Bowen, Vladimir Coufal and new signing Nayef Aguerd were among the international players to return at the Madejski Stadium.
West Ham will manage to avoid the extreme London heat on Tuesday, but Moyes can still be expected to make wholesale changes throughout as Lukasz Fabianski and Alphonse Areola resume their battle for the gloves.
Rangers possible starting lineup:
McGregor; Tavernier, Goldson, Souttar, Barisic; Jack, Kamara, Lundstram; Lawrence, Colak, Kent
West Ham United possible starting lineup:
Fabianski; Coufal, Zouma, Aguerd, Cresswell; Rice, Downes; Bowen, Fornals, Benrahma; Antonio
We say: Rangers 1-1 West Ham United
Both Van Bronckhorst and Moyes will make full use of their squads as ever this week, but the Hammers' draw with Reading showed that the international crop still need a bit of time to get re-acquainted with domestic football.