Taylor recently became incensed with Parcells during a recent visit to team headquarters, according to the Miami Herald. Taylor popped in on the Dolphins' executive vice president while he was watching tape, but the newspaper said Parcells ignored Taylor without speaking a word to him.
Taylor was taking a break from "Dancing With the Stars" when he stopped in to visit Dolphins players in South Florida. According to the Herald, after receiving a warm reception from his teammates, Taylor decided to seek out Parcells.
But according to the Herald, Parcells had no interest in talking to Taylor. Parcells even looked at Taylor, the newspaper reported, before going back to watching tape.
Through his dancing, Taylor has become a network TV star this offseason, but Parcells is unhappy his best player has been focused on a budding Hollywood career rather than being back in Florida working out with teammates.
According to the Herald, Parcells and Taylor have barely spoken to one another this offseason.
Taylor was the subject of trade speculation throughout the weekend. But when the NFL draft ended Sunday, general manager Jeff Ireland denied the Dolphins were eager to part with Taylor.
"We want the guy back," Ireland said.
Jacksonville Jaguars coach Jack Del Rio said his team pursued a deal with Miami, but the Dolphins took Taylor off the trading block.
"We talked," Del Rio said. "They had a certain price in mind, and nobody in the league was interested in that price. They like the player, and they're going to keep him. There's nothing wrong with that."
The Tampa Bay Buccaneers denied rumors they were close to acquiring the six-time Pro Bowl defensive end.
Signals from the Dolphins have been decidedly mixed. On Saturday, owner Wayne Huizenga said the team was open to trading Taylor. Miami drafted two defensive ends as potential replacements -- Clemson's Phillip Merling in the second round, and Hampton's Kendall Langford in the third round.
But when asked about a pledge last month by Parcells that Taylor wouldn't be traded, Ireland said, "Nothing has changed."
Taylor had 11 sacks last season to increase his career total to 117, third among active players. He made the Pro Bowl and was chosen NFL Man of the Year.
"Dancing With the Stars" could keep Taylor in California until May 20. He has said he wants to remain with the Dolphins, but at age 33, he also likes the idea of being traded to a contending team.
When asked about the new regime's relationship with Taylor, Ireland said: "Hopefully it's pretty good."
Information from The Associated Press was used in this report.