"There's no truth in it whatsoever," Pulis told BBC Radio Stoke. "They've got to fill their papers and fill their television programmes.
"I'll do all of my business with the clubs that I'm dealing with."
Stoke have been quiet in the transfer market during pre-season, bringing in teenager Florent Cuvelier from Portsmouth and experienced goalkeeper Carlo Nash, who was released by Everton in May.
The Potters have also been linked with moves for Manchester City pair Roque Santa Cruz and Jo as Pulis looks to add more firepower to a squad which managed just 34 goals in the Premier League in 2009/10.
Cole, who has won all six of his international caps under Fabio Capello, scored 10 times for the Hammers last season and netted the only goal in their 1-0 victory over Ipswich on Saturday.
Meanwhile, Pulis has not ruled James Beattie or Dave Kitson out of his plans for the new season.
If we need them for next season, we need them for next season
Tony Pulis on the futures of Dave Kitson and James Beattie
The forward pair are likely to be allowed to leave the Britannia Stadium if the club receives a suitable offer.
"They're both Stoke City players, we still pay them and at the moment they're working as hard as the others to keep fit," said the Stoke manager.
"If we need them for next season, we need them for next season."
The Potters beat Burnley 2-1 in a friendly at Huddersfield's Galpharm Stadium on Saturday, with Tuncay and Michael Tonge scoring the goals.
Source: BBC Sport
Source: BBC Sport