The on-loan Derby forward has played a key role in the Blues’ climb off the foot of the Championship table.
His arrival into Appleton’s starting line-up has coincided with seven points from the past four games as Pompey fight to remain in the division.
Maguire was once again impressive in Tuesday night’s outstanding 2-0 triumph over Hull, scoring the opener.
In accordance with his initial 28-day emergency loan from Pride Park, the Scot has another week remaining on the south coast.
However, once that expires, Appleton is keen for his loan to be extended to the season’s end.
That will be down to the Rams, though, and then for the Football League to ratify.
But Appleton is optimistic the 23-year-old will stay.
He said: ‘Hopefully, we can keep Chris until the end of the season, although obviously the Football League need to let it be renewed.
‘I am always worried that teams might want my players back but, hopefully, that won’t be the situation. He couldn’t get in their team in the first place.
‘The original agreement (with Derby) was to have him for the rest of the season.
‘They were quite happy for him to stay until the end of the season, so I would be disappointed if they go back on their word.
‘He had a fantastic night against Hull. I felt he and Luke Varney were the catalyst for everything that was good about the team.
‘It started from the front, it got us on the front foot and there were some really strong performances.
‘But don’t play him up too much, I don’t want him getting called back!’
Maguire has now scored twice in five games after arriving at the start of the month.
Before then he had failed to make a Derby appearance since November when, coincidentally, he came off the bench against Hull.
Now he is revelling in regular first-team football at Fratton Park and Appleton has been impressed with his contribution.
He added: ‘I was aware of his qualities long before he came down to England with Derby, similar to Scott Allan.
‘The thing I really like about Chris is he is a player who really enjoys playing the game. He plays with a smile on his face.
‘Not only does he enjoy scoring goals but I think he gets the same kick out of blocking the ball down the line from the centre half or full-back. The fans appreciate that.
‘Why he has not been playing for Derby has got nothing to do with me.
‘All I know is he has got quality, I like the player and jumped at the opportunity to work with him.
‘I tried to get him in January but it didn’t quite happen. Then again a lot sooner than we actually did but for whatever reason it didn’t happen.
‘But I am glad he is here now. He’s enjoying his football and the opportunity to show he is a talent.’