The Bluebirds currently sit third in the Championship, with Matthews beginning to make a name for himself in defence, having made 14 league appearances in 2009/10, scoring once.
As a result, the 17-year-old is already being linked with a move to the Premier League, and Jones feels it would be wrong for him to get in the way of what could be the biggest move of such a young player's career.
Old Trafford supremo Sir Alex Ferguson faces a hectic Christmas period with the majority of his defensive ranks sidelined, meaning the door could be ajar for Matthews to make the step up.
"We have always maintained that if the right offer comes in for one of our players, and it is the right offer for this club we would listen," Jones told Wales online.
"It is very difficult if Manchester United are interested, for us to stay here and see out your contract with Cardiff and forget about going into the Premier League with one of the best clubs in Europe."
Cardiff have produced several stars in recent years but have struggled to retain their services when bigger clubs have come calling.
And with speculation again suggesting that Joe Ledley will depart for pastures new, Jones insists he needs to try and hold on to his most promising talents if they are to achieve their dream of promotion this season.
"We had that problem with Aaron Ramsey when Arsenal came in," he said.
"If there is an offer made, then that will be done and we will look at it if it comes in writing."
