However, Martinez has confirmed that there have been no approaches.
"It's a rumour and we'll leave it there. We have spoken enough in the past about potential interest and I always mention the same, we take it as a footballing compliment and we move on," the Spaniard told Sky Sports News.
"All we want from Ross now is to be able to get him fully fit and get him ready to enjoy his football and to help the team and we're looking forward to that day."
Barkley is currently injured but is ahead of schedule in recovering.