The former Blackburn supremo Williams was appointed by incoming owner Guochuan Lai in the summer following his buy out of the club from Jeremy Peace.
There was speculation that Williams and head coach Pulis had a falling out over the club's failure to bring in an experienced big-name midfielder and striker before the deadline on September 1.
It was also suggested that Williams engineered a season-long loan deal for Everton full-back Brendan Galloway without Pulis' blessing.
However, Williams rubbished those claims and insisted that the club will do all they can to bring in Pulis' targets in January with the manager having the final say over all comings and goings.
He said: "I could never conceive of signing a player the manager didn't want. We wouldn't do it.
"One thing a manager quite rightly has is control of team selection and why would you want to sign players he wouldn't want?
"Brendan Galloway for example – I read last week that he was not a ‘pick’ of Tony's. I don't know where that came from.
"I can even remember sitting in the room with Tony watching tapes of the lad and Tony saying how much he liked him.
"It would be plainly daft to start thrusting players on Tony that he did not want and that will not happen."