The highly-rated teenager has been at the City Ground since November 25 as Arsenal look to get him match-fit again after nine months out with a broken leg.
Until making his first start against Derby on Wednesday night, Ramsey had managed just 45 minutes from two second-half substitute appearances in games against Leicester and Crystal Palace - although Forest did have two matches postponed this month.
The midfielder played an hour of the 5-2 victory over Derby before he was substituted and he is eligible for just two more games before his loan expires on January 3.
"It was nice to get Aaron Ramsay on the pitch. He is getting fitter and better and he had a decent performance," said Davies.
"I have given a recommendation to the board with regards to him, we'll see what happens."
Source: PA
Source: PA