HITC Sport understands a decision on the Atletico Madrid forward's work permit application will be made on Wednesday.
HITC Sport has been told that The Hammers are not entirely confident that under new Home Office/Football Association regulations they will be successful.
The 22-year-old has already agreed terms with West Ham, and the two clubs have finalised an agreement on a season-long loan.
However, there is no clause to make the deal permanent - it is a straight loan and that is one of the issues that will count against him under new rules.
The regulations look less favourable for loans, and especially ones which do not have a clause to buy at the end. Also, technically, Jimenez falls short of the criteria, but that was mainly down to him missing the recent Gold Cup.
However, having already played in the Copa America, Atletico Madrid pulled him out of the second tournament in order for him to meet European law of having enough holiday before he began work training with them again.
"It is up in the air," the source told HITC Sport.
"The old system, he would have sailed through given the calibre of player he is - but now it is more points based, but there could be legal ramifications with this one as the only reason he does not meet criteria was because he had to miss the Gold Cup - it should never be in doubt for a player like this."
The Premier League are keeping a very close eye on the Jimenez situation as his case could have big consequences for the English game as a whole.