The Worksop star endured a tough second round at the Hoylake course, carding a four-over-par 76 to finish three-over for the tournament.
The top 70 players, plus ties for the last qualifying position, will make it through to the weekend.
Currently, the cut is at two-over, which would see Westwood miss out.
But with many players, including overnight leader Rory McIlroy still to complete or even start their second rounds and the weather forecast remaining unpredictable with the threat of thunderstorms still in the air, there is every chance the cut line could go out to a bigger figure and allow Westwood to get in for the weekend.
Westwood battled hard in tougher afternoon conditions to card a 71 on day one.
And he faced difficult conditions again for his morning start today (Friday) with gusting wind making scoring difficult.
A poor start saw him drop shots on the second and fourth holes before an ugly double-bogey six on the eighth left him three-over for the championship after taking 39 shots for the front nine.
A first birdie of the day on the 11th got him back to two-over and looking better for making the cut again.
But he gave the shot back again with a bogey at the 14th and was unable to find another birdie in the remaining four holes, despite two of them being par-fives.
Westwood is not the only big name to have struggled over the Hoylake links. Masters champion Bubba Watson is also sweating on making the cut after finishing at four-over, while former champion Ernie Els is definitely out at eight-over.
The top round of the day so far has come from South African George Coetzee, who came in with a 69 to be one off the lead at five-under.