Striker Parkin, on loan from Cardiff, and Wolves defender Reckford have played a key role as the Iron secured back-to-back wins last week.
Midfielder Josh Walker has already extended his loan spell at the club, while Watford team-mate David Mirfin arrived at the end of last month until the end of the season.
"The aim is to try and extend everybody's loan period," Knill told the club's official website. "But obviously we need to speak to the parent clubs as soon as possible to make that happen.
"We have set some targets that we want to get to and those players are key to achieving that. They're playing well so the last thing that you want is to lose them.
"So if it's possible then we will try and keep them. If not we will have to try and get somebody else."
