Reports in several media outlets on Thursday allege the winger twice broke a club curfew ahead of games and that he has struggled to get into the team as a result.
But Pennant took to Twitter on Thursday afternoon to refute the claims, saying: "I'm all over #skysports saying I've been fined when it's not true the gaffa is going mad.
"So to all the stoke fans and for the record there is no problem with me and TP I have not been fined and we haven't fallen out at all.
"I respect our manager and I respect my team mates and most off I respect the club and fans."
Pennant joined Stoke last summer with a reputation for getting into trouble off the pitch, and rumours of a rift with Pulis first surfaced in December.
He was left out of the squad for matches against Everton and Tottenham and then found himself on the bench for the Europa League clash with Besiktas despite Pulis taking a squad of only 15 players to Istanbul.
Pennant has started only one match in the last month, the 1-0 home defeat by Valencia in the Europa League last 32, with academy graduate Ryan Shotton often preferred on the right of midfield despite being a full-back by trade.
Stoke have so far declined to comment on the issue.