Peacock-Farrell made his senior debut for Leeds on Tuesday evening against QPR, and came close to keeping a clean sheet, conceding a penalty in the 87th minute after a solid performance.
The 19-year-old is out of contract in the summer, making it an anxious time for the Whites, as Premier League interest increases, with Tottenham and Everton among those also interested.
While any interested side would have to pay a small compensation figure to be determined by a tribunal, snapping up a goalkeeper with Peacock-Farrell's potential makes a lot of sense.
West Ham have one of the best academy's in the country, with their development squad in the final of the under-21 cup, after beating Liverpool in the semi.
Yet unlike fellow interested club Tottenham, who have two international goalkeepers in his path in Hugo Lloris and Michel Vorm, joining West Ham may be less daunting for Peacock-Farrell.
Number one goalkeeper is uncapped Spaniard, Adrian, who made his 100th appearance for the Hammers last weekend.
He will not be dislodged easily, but behind the 29-year-old, there could be a way in. Second choice is Darren Randolph, who will go to Euro 2016 as Ireland's number one after the injury to Newcastle's Rob Elliott.
This will put him in the shop window and give him a taste of first team action which could make him willing to move on this summer. For the Hammers he has been less than convincing, conceding four goals against Bournemouth earlier this season.
Behind him is 23-year-old Swiss stopper Raphael Spiegel, who is yet to make an appearance for the first team this season. He has a contract until 2018, but Peacock-Farrell would have to hope that he could seize the initiative from him in the battle for places.
There are no easy Premier League landing spots for a teenage goalkeeper from the Championship, but Peacock-Farrell fits the mould for what teams are looking for. He is young, has already made his debut, is English so fits the homegrown quota, and has huge potential.
The Hammers raided Leeds to sign Sam Byram earlier this year, who will be able to give first hand feedback on the young goalkeeper, and could even play a role in convincing his pal that moving to East London is the right move for him.