Per the source, the Hammers are looking for reinforcements upfront following the injury to record signing Andrew Ayew who has been ruled out for four-months.
The East London based outfit do not want to splash the cash again after spending £20 million on the Ghanian international and will pursue a loan deal instead.
Gunners boss Arsene Wenger has had no luck in signing a striker this summer after being turned down by Jamie Vardy and having talks with Lyon forward Lacazette stall.
Wenger is running out of time and could be forced into making a move for Bony who City have instructed to find a new club.
Turkish champions Besiktas are however, currently favourites to sign Bony after club president Fikret Orman entered talks with City over a loan deal.
Bony fell out of favour at City but did score 35 times in 70 appearances for Swansea City in all competitions.