The 29-year-old, who made his first start for the club in the 0-0 draw with Newcastle at the weekend, has insisted, however, that the Hammers were his first choice.
"There were things going on in the background and Newcastle enquired about me. But it sounds like their owners are similar to Liverpool on transfer fees and wages and the player's age," Downing told the Daily Mirror.
"That all comes into the equation, and I think that was obviously a problem for Alan Pardew. It was a move I was interested in and I looked at it, but when I spoke to Sam Allardyce he wanted me straight away. He pushed the boat out to get me, and there's nothing more you want as a player."
Downing has also previously played for Aston Villa.