Giampaolo agreed over the weekend to take over at Serie A side Cesena after Massimo Ficcadenti left by mutual consent despite keeping them in the top flight.
Media reports said Giampaolo had since held talks with Roma but he has denied changing his mind.
"I am a man of my word and I shook the president's hand so I 100 percent feel like the Cesena coach," Giampaolo told reporters.
"The chat with Roma did not regard the manager's position."
Barcelona B coach and former Spain midfielder Enrique now looks poised to take over at American-owned Roma, who had been managed on an interim basis by youth team boss Vincenzo Montella since Claudio Ranieri's resignation in mid-season.
Former Chelsea boss Carlo Ancelotti had been linked with Roma but has said he is taking a year off while Didier Deschamps is staying at Olympique Marseille.
Catania have said Montella is close to being named their new coach.
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