The Spanish shot-stopper says his compatriot would be a great addition to help the club defend their Premier League title, but insists any decision rests with the Barcelona star
The 22-year-old playmaker swapped Barcelona for the Bundesliga rather than move to Old Trafford, and the Liga champions have so far resisted United's bids for Fabregas, leaving David Moyes without a major summer signing so far.
And while the 22-year-old shot-stopper's efforts to convince his young Spain team-mate to join him in England were fruitless, De Gea hopes to persuade Fabregas – but insists the former Arsenal star must decide his future himself.
"[Fabgreas] has to make a decision to stay or come to us," De Gea told Marca.
"He would be a great signing, and would help us to improve."
United's attempts to buy Thiago gathered pace early in the summer with De Gea fuelling speculation as the duo played together and won the Euro Under-21 tournament with ease, but the midfielder elected to join Guardiola in Germany.
"Yes, I tried to convince him, but it could not be," he said.
"He would have been a good signing. He decided for Bayern who are a very good club, and I'm sure he'll do very well."
Fabregas has endured a testing return to the Nou Camp since moving back to his boyhood club from Arsenal in 2011; he notched 11 goals and 11 assists from 32 La Liga appearances last season but has struggled in the eyes of the fans.
Goal exclusively revealed on Monday that Moyes will look to former club Everton to secure the signature of midfielder Marouane Fellaini if a deal for Fabregas proves unsuccessful.