Milner has been a hit in the Premier League this season and has been linked with a move to Manchester United.
O’Neill said: “I wouldn’t be surprised that James and Ashley have attracted attention from the very best football clubs in the land and possibly one or two in Europe as well.
“I don’t think they would have any problems adjusting to one of those clubs at all. The two of them have matured now, not just on the field but off it as well. Their games have improved immensely.
“Sometimes people think that Ashley Young has maybe not performed the same as last season. That’s not my view. I think he’s better than ever.
“James Milner has been a revelation, he’s just a different player. He’s stepped in 20 yards from the wing into the middle and I knew he was capable of doing that. He’s been absolutely fantastic. He’s got the energy, he’s got the determination and more important than anything he’s got the ability.
“Wayne Rooney would undoubtedly deserve to win the player of the year, if that was the case then James would deserve young player of the year, he’s been brilliant.”