The Championship team are hoping that the talented young full-back commits his future to the club but concede that they would not stop him completing a move to the Red Devils
The 20-year-old has been strongly linked with a summer switch to Old Trafford to provide added competition for the full-back spots, and Parish has admitted the move could well happen.
"We haven't agreed anything with anybody and we still have a contract offer on the table for Nathaniel," Parish told the Evening Standard.
"We have a good relationship with both him and his agent and I think he is enjoying his football here and can see the club are going forward. But if there is a deal to be done with Manchester United, it would be hard to stand in the kid's way.
“If our young players are to leave, then at least we want them to go onto something bigger and better - and Manchester United are who they are."
Manchester United's next match, away to Blackburn on April 2, is 7/5 with Sportingbet to go over 3.5 goals.
Clyne has made over 100 appearances for the Championship side since breaking into the first team and won the club’s Player of the Year award in 2011.