Gayle joined the Shrews at the end of last month on a deal until January 3, 2013.
The 20-year-old's stay at Greenhous Meadow has been disrupted by a groin injury but he has demonstrated his versatility on both the right and left side of defence in the two games he has played for Graham Turner's team.
Turner told the Shropshire Star: "Cameron has done well and we will extend that if we can.
"I get the impression he is enjoying himself and I get the impression West Brom are pleased he's playing.
"We've got a good relationship with them, so I would like to think all parties will come together to extend the loan."