The Premier League champions have long been linked with the 20-year-old midfielder - who has recently returned from a knee ligament injury.
Barkley, as well as bolstering Manuel Pellegrini's midfield ranks, would also add a third Englishman to City's squad and boost their homegrown quota.
The likes of Wayne Rooney and Joleon Lescott have previously been taken from Everton in big-money transfers, but Martinez insists the club do not need to sell star players to balance the books.
"Everything is there for [clubs like Manchester City] to buy. It makes a difference if you have a year left or five years left [on their contract] but in the same way, we are a club that does not have to sell," he told the Liverpool Echo.
"We have gone past that period and the football club is in a fantastic moment financially. We showed that in the last transfer window and everything will be football decisions.
"That gives me a real peace of mind and tranquillity of making sure the players at the club keep progressing, keep getting better and stronger and that is a good position to be in.
"It doesn't worry me at all. The loyalty that the players had many years ago is out of the game. But as a football club, we don't need to sell and that makes every decision a football one for the good of the club, so I’m very relaxed about it."
Barkley is one of a handful of young players to impress for Everton since Martinez took over, alongside the likes of John Stones, Romelu Lukaku and James McCarthy.
Martinez welcomes the attention that Barkley is attracting, claiming it demonstrates how impressive his form has been.
"All the speculation and talk is positive. Because you don’t get any of that when your players are not playing well or they haven’t got potential," he added.
"I'd rather have lots of teams showing interest in our players because we don’t have to be forced to do things that we don’t want."
