The defensive midfielder fell out of favor with former Middlesbrough coach Gareth Southgate and is yet to enjoy a change of fortune under new boss Strachan.
Shawky, who joined then Premier League side Boro (now playing in the second division) from Ahli in the summer of 2007, hasn't made any competitive appearance with the team so far this season.
He is likely to seek a new move when the transfer window reopens in January after Strachan highlighted his need of new midfielders.
"I think every clubs wants to be active in the transfer market," the Scottish manager told Middlesbrough's official website.
"We've got a very small squad, there's no doubt about that. We're short upfront and we're short in midfield. We have enough defenders.
"We can only look at loans right now but January is different. We'll be able to bring people in on permanent deals in January and then the summer."
The club have already signed former Aston Villa midfielder Isaiah Osbourne on a two-month loan deal.
Shawky has linked up with his Egypt teammates as they gear up for the crucial World Cup qualifier at home to Algeria on Saturday.
He is a regular starter for the Pharaohs despite lack of first-team action with Middlesbrough.