Despite ending his long-term association with the Premier League giants back in the summer, De Gea remains without a new club.
A wide array of teams from England and abroad are said to have expressed an interest without coming close to getting a deal over the line.
However, according to the Daily Mail, Al Shabab have been able to begin negotiations with the Spain international in recent days.
Although Al Shabab find themselves down in 11th position in the Saudi Pro League standings, they have been heavily linked with several notable names in January, including Sevilla's Ivan Rakitic and Newcastle United's Miguel Almiron.
As it stands, it is unclear whether De Gea will be tempted into a switch to the Middle East or continue to bide his time in hope of a move to a high-profile European club.
Meanwhile, Blackburn Rovers reportedly emerge as the latest club to show an interest in signing Liverpool defender Nat Phillips.
The centre-back has recently returned to Anfield after an unproductive loan stint with Celtic, where he made just eight appearances in all competitions.
With the 26-year-old having failed to impress north of the border, the likelihood is that he will have to settle for another period in the Championship for the second half of the season.
Leeds United have been linked with Phillips in recent days, but the Daily Mail suggests that they have competition in the form of Blackburn.
Jon Dahl Tomasson's side have struggled at the back in recent months and now possess the worst defensive record in the second tier, conceding 53 goals in 28 games.
While the possibility remains that Phillips could be kept at Liverpool as cover for the injured Joel Matip, that seems unlikely at this stage when first-team football can be secured through a loan elsewhere.
Arsenal could receive a boost in their efforts to boost their FFP position before the closure of the January window with the sale of Cedric Soares.
The 32-year-old has not made a single Premier League outing all season, instead being reduced to two appearances in the Champions League and EFL Cup respectively.
With less than six months remaining on his contract and no prospect of a renewal, the Portuguese will depart the Emirates Stadium in January or the summer.
According to the Evening Standard, Galatasaray are interested in getting a deal over the line before the transfer deadline.
Sacha Boey has completed a switch to Bayern Munich after starring in the right-back role, leading to the Turkish giants requiring a replacement as soon as possible.
The report adds that any exit for Soares would be on a permanent basis, something that may still attract Galatasaray even though they may consider a longer-term option in the summer.