Turner watched Middlesbrough winger Reach cap an impressive debut performance with a goal in Town's 2-0 win over Swindon in mid-August.
However, the 20-year-old has failed to match the same heights since and started Saturday's 1-1 draw at Crawley on the bench.
But Turner has decided to hand Reach an extended stay at the Greenhous Meadow.
"We've spoken to Middlesbrough and agreed that Adam will be staying for at least another month, which is good news," Turner told the club's official website.
"With Adam not being a regular starter I can see his frustration but he has a lot of ability and has already got a goal for us."