The veteran midfielder, on loan from Manchester City, is keeping his options open as his spell at Goodison Park comes to an end.
The 33-year-old has been a shining light as the Toffees have launched an unlikely assault on the top four and will play the final home game of his short-term spell against Manchester United on Sunday, as he is ineligible to face his parent club in the Toffees' only other remaining Goodison Park outing of the season.
“If the club offer me a contract and show me they want me, then it is a possibility,” he told reporters. “It won’t be a case of waving to the fans on Sunday. That would be like saying goodbye before I’ve made any decision. I’m just desperate to finish the season on a high.
“Roberto has been brilliant. I’ve learned so much from him, he’s got great ideas all the time that are ahead of the game. Even at 33, I’m still learning tactical stuff from him.”
Barry held discussions with Manchester City manager Manuel Pellegrini before leaving City, telling the manager that he could become a key part of his squad in 2013-14, but holds no regrets over his decision to leave the Etihad Stadium.
“I told him that I could compete for a place at City and that he was wrong to decide I wasn’t good enough,” Barry said. “You’ve got to back yourself even if your face doesn’t fit. But once somebody has made up their mind, that’s it. Any rejection hurts in life but as soon as I came through the doors at Everton, it was all forgotten about.
“I knew I was leaving a team that had every chance of winning silverware. I thought they would win the Premier League. But for me, playing regularly and being happy was going to make for a better life. I think that decision to move has been the right one.”