David Moyes is keen to bolster his squad with a new centre-forward this summer to provide competition for Michail Antonio, while he is also in the market for a centre-midfielder following the retirement of club legend Mark Noble.
The Hammers have held an interest in Broja throughout this summer after the 20-year-old enjoyed a successful loan spell with Southampton last season, scoring nine goals in 38 appearances across all competitions.
According to Sky Sports News, West Ham have made an £30m offer to Chelsea for Broja, which includes a £25m upfront payment plus £5m in add-ons.
Negotiations are allegedly ongoing between the two London clubs over the Albania international, although Chelsea boss Thomas Tuchel has recently revealed that the striker is part of his plans and is not for sale.
The Hammers are expected to face competition for Broja's signature from a host of other European clubs, including the likes of Napoli, Everton, Newcastle United and Southampton.
Broja, who is currently training with Tuchel's squad on their pre-season tour of the USA, penned a new long-term contract with the Blues until 2026 last summer.
Meanwhile, the same report also claims that West Ham have lodged an improved €38m (£32.3m) bid plus add-ons for Lille's 6ft 3in midfielder Onana, having previously seen two offers knocked back by the Ligue 1 outfit.
Lille are believed to be "seriously considering" the Hammers' new proposal, which would see them make a considerable profit on the 20-year-old who they signed for just €7m (£6m) from Hamburg last summer.
Onana started only 15 of his 41 appearances for Les Douges last season, but he was still able to impress Belgium boss Roberto Martinez who handed the youngster his international debut against the Netherlands last month.
Furthermore, the East Londoners have made a €40m (£34m) bid plus add-ons for Sassuolo's 23-year-old striker Gianluca Scamacca according to the Italian club's CEO Giovanni Carnevali.
Speaking to the media, via journalist Fabrizio Romano, Carnevali said: "West Ham are offering €40m for Scamacca and Paris Saint-Germain offering €35m.
"There are also some add-ons as difference. We don't need to sell, so we will see - there's no agreement with any club now."
Scamacca, who scored 16 Serie A goals in 36 appearances last season, is believed to be one of Moyes's top striker targets this summer along with Broja.
West Ham have already made three signings this summer, recruiting centre-back Nayef Aguerd from Rennes for £30m, goalkeeper Alphonse Areola from PSG for £7.75m and midfielder Flynn Downes from Swansea City for a fee which could rise to around £14m.