Rangers are looking to bring in a new midfielder this month.
Rangers missed out on signing Toumani Diagouraga, with the Frenchman opting to sign for Leeds United yesterday.
There Gers failed to meet his asking price, and they remain in the market looking for a new midfielder, in the last week of the transfer window.
With Rangers not willing to raise their bid for the former Brentford man, it is clear they are working under some financial restrictions, and manager Mark Warburton should be tempted to look at utilising the loan market again.
Rangers have already brought in Gedion Zelalem, Dominic Ball and Nathan Oduwa, and whilst the latter has returned to Spurs, the Gers have enjoyed varying levels of success from all three.
Cullen made his debut for the Hammers earlier this season, playing in three Europa League qualifying games, before coming on as a late substitute against Liverpool in the Premier League.
He has occasionally been named on the bench in the league, but his season has been spent in the Under-21team, and the midfielder needs to be playing at a more competitive level to ensure his development does not stagnate.
The 19-year-old has all the traits to excel in the Scottish Championship, and it would be a great move if Rangers could agree the youngster.
He shares many of the same qualities as Diagouraga, being a technically gifted midfielder capable at the defensive work as much as the offensive work, and being able to match up physically with many of his older competitors. He can sit deep as a holding player, or push further forward and provide an energetic box-to-box presence.
Cullen needs to be playing at a competitive level every week to ensure his development progresses in the correct manner, and Rangers should look to bring him in on a loan deal before the end of this month.