The Cottagers would certainly be in the running to secure Loftus-Cheek for next term and beyond - if they stayed in the Premier League.
The midfielder has been excellent for Parker's team this season, with the 25-year-old showing his quality in the middle of the park.
"Would I try to sign him permanently? Yes, of course," Parker told reporters.
"Ruben's been a fantastic addition. We've seen him grow immensely from the start of the season until now. He's transformed really.
"At the moment it's just this year for Ruben and we're looking at the next 12 games and where he can get better.
"But certainly, from my side, if there's an opportunity to do it [a permanent move], we'd be more than happy to try and make it happen."