After more than ten years at Old Trafford, De Gea left United in the summer, having won the Premier League Golden Glove in his last year.
He was let go after failing to agree on contract terms with the club and was replaced by Inter Milan's goalkeeper Andre Onana.
The Spanish goalkeeper has been without a club since leaving the Red Devils but could be close to joining a new club soon.
De Gea on the move
De Gea, a free agent, has been linked with a move to several clubs; rumours have it that Al-Nassr contacted the former Spain international back in November.
However, it has been reported by the Daily Mail that the Saudi Arabian side, Al-Shabab are discussing with De Gea about a possible transfer move.
Al-Shabab are also in talks to get Miguel Almiron of Newcastle and are in the process of signing Ivan Rakitic from Sevilla.
Signing David De Gea to the set of transfers they are looking to complete would be a history-breaking moment for the club.
They are also looking to sign Chelsea winger Hakim Ziyech who is currently on loan at Galatasaray.
Al-Shabab, who had only won one of their previous seven league games before the winter break, are presently ranked eleventh in the Saudi first division.