Hammers boss Avram Grant said: "I have nothing to say until the deals are done. But I like Steve. I worked with him at Chelsea, he never let me down."
Grant had hoped to bolster the midfield with his team only one point above the Premier League relegation zone.
With Sidwell still to put pen to paper, Grant was left a little bemused as to why the deal was still to be concluded.
"I don't know, I am not dealing with the situation and I don't have any news but we are continuing to look at this situation," the Israeli told Sky Sports.
Regarding other potential acquisitions in the current transfer window, Grant added: "January stories, part of them are true and part are not.
We have so many central midfielders. This would either be good or bad
Up the hammers
"We have followed many players like many clubs, we are following players to make us strong, but we will not bring in 15 players, not even five."
Sidwell has played only four league games for Villa this season and was signed from Chelsea for £5m in 2008.
He began his professional career with Arsenal in 2001 and has also played for Brentford, Brighton and Reading.
Having climbed off the bottom of the bottom of the table, West Ham face a trip to Newcastle on Wednesday where they will come up against former Hammers boss Alan Pardew.
Grant, looking to build on a run of four unbeaten matches, said: "The feeling is good but there is a long way to go."
Source: BBC Sport
Source: BBC Sport