The Hammers will play away at Maltese minnows Birkirkara tomorrow night and hold a 1-0 advantage from the first leg at Upton Park.
They are favourites to progress to the third qualifying round where they will face either Inverness or Romanian side Astra Giurgiu.
The odds are stacked against the Scottish side, though, after they suffered a 1-0 reverse in the first leg last week.
'"I'd love to see the Inverness supporters strutting their stuff down in London. But it's dangerous to look too far in front of us.
"It adds a little bit of spice to it; hopefully we can take care of business."
Hammers must be wary of cup specialists
Should both teams progress, the Hammers will need to be wary of their opponents from north of the border.
Inverness are coming off the back of the best season in the club's history, finishing third in the Scottish Premiership and winning the Scottish Cup.
Their ground only holds 7,800 and was hastily expanded by a local firm to meet top-flight regulations.
They are notorious cup specialists too.
Unforgettable victories over Celtic in 2000 and 2003, one of which saw them triumph 3–1 at Celtic Park and resulted in the famous headline "Super Caley Go Ballistic Celtic Are Atrocious" in The Sun which is now framed in the foyer of their stadium.
Red hot favourites but a unique opportunity
Comparatively, though, Slaven Bilic's side will be red hot favourites given the size and strength of their squad which is filled with internationals.
West Ham have already spent more than £25 million this summer bringing in seven new signings.
It would also offer Inverness the unique chance to play at West Ham's Boleyn Ground home of 112 years for the first and last time before they depart for the 54,000 seater Olympic Stadium next summer.
However, the Scottish side will have been encouraged by what they saw if they watched the Irons' first leg game against Birkirkara, where they toiled desperately for a slender victory.