Stoke have been slow in the transfer market so far this summer, capturing only Portsmouth Academy star Florent Cuvellier and out-of-contract goalkeeper Carlo Nash, but Pulis is willing to bide his time in his pursuit of his targets.
It had been reported in the national press that offers had been made for O'Neil and Rodallega, both of whom have been on Pulis' hitlist in the past, but the Potters boss insists there has been no contact with either Middlesbrough or Wigan.
"It's agents and other people talking about Gary," he said. "There's been no contact between the clubs."
Boro are keen to shift O'Neil on this summer and a number of agents are working to engineer him a move away from the Riverside Stadium but there have been no takers as of yet.
Rodallega, meanwhile, was first linked with a move to Stoke in January but Pulis is adamant the striker is not in his thoughts anymore.
"Again, I've not been in touch with anybody at Wigan," he added. "But it's lovely people are thinking about the targets we are not really looking at.
"We have been working diligently to get deals done, but it's not gone for us yet."
Stoke are still chasing West Ham duo Carlton Cole and Mark Noble, while a full-back, right midfielder and second striker could also be brought in depending on who leaves the Britannia Stadium.