The sides meet at the Stadium of Light on Wednesday evening with the 46-year-old Uruguayan, who refused to be drawn into a war of words with predecessor Paolo Di Canio, baring his teeth at the Potters.
Poyet said: "I am pleased that in the local newspaper, we didn't throw any rumours about us being interested in any Stoke player, because that's what they have done for the last week.
"No-one from Stoke, directors or anyone from them, has made any formal approach or any offer, so for them to be linked with two very important players for us before the game is a little bit disappointing."
City boss Mark Hughes has been linked with a move for Cattermole for several weeks, but admitted over the weekend that the Black Cats' progression to the Capital One Cup final made that unlikely.
Poyet said: "He [Hughes] didn't call me. Some people would say the manager normally would call to say when they want a player of the other team.
"But he didn't call me, of that I can assure you."
Cattermole's future has been thrown into doubt by Sunderland's interest in Brighton midfielder Liam Bridcutt, who finds himself in limbo after having a transfer request refused.
The Black Cats' offers for Bridcutt and winger Will Buckley remain on the table with three days of the January transfer window remaining, and progress on that front could yet prompt a change in their stance.
However, Poyet, who revealed he is "very, very close" to landing Internacional's Argentinian striker Ignacio Scocco, has no intention of allowing matters to run into the final few hours before Friday's 11pm deadline.
Asked if there would be a cut-off point, the former Brighton boss said: "It probably would be Thursday. I am not going to put a time-frame on it, but I would like not to be here on Friday."
Poyet was taking a more diplomatic line, however, when asked about Di Canio's weekend broadside, in which he branded the club "weak" and some of its players "cowards", and insisted Sunderland were no better off now than they day he was relieved of his duties, prompting a dismissive statement from the Stadium of Light hierarchy on Monday.
His successor said: "I think the club was spot-on with its statement and I will maintain that. We will go with the club and the players have been respecting that as well. It's the best way for us.
"Me, I am very critical with myself and I analyse myself first. Every game after winning or losing, I check myself, what I did well, what I didn't do well under my understanding of football, whether the players reacted to what I said or not.
"I am just trying to keep improving and to keep getting better, not only as a team, but me as a manager as well.
"That's the best way for us to make sure we get to the situation that we want at the end of the season, which is being in the Barclays Premier League."