O’Neill spoke out after Solihull-born Gardner put his off-field issues to one side to come on as a substitute to score a 25-yard screamer against Swansea that effectively secured his team all three points after Sunderland were left hanging on to a slender lead after Stephane Sessegnon had opened the scoring for the Black Cats.
“Craig has become a bit of a favourite here and that isn’t just to do with his goal,” O’Neill told reporters at his post-match press conference.
“We know his capabilities and no one wants him to leave the club and I am hoping that homesickness is something that he can look at in a month or two or a year or two or perhaps a decade or two.
“At this moment there is no concrete offer. There is interest from other Premier League teams in around that area but there has been nothing concrete and we wouldn’t want him to be leaving.
“I have not thought about an immediate replacement at this moment but time is running out and we want him to stay.”
O’Neill, who worked with Gardner during their days together at Aston Villa, added: “When the ball came to him I knew it would end up in the back of the net because I worked with him at Aston Villa.
“At the moment Craig is unlucky not to be in the starting line-up but chances are he will be playing next week. He has done very well for us. He has played out of position which he has been happy to do for me before and he said if he had to go play as an emergency full-back again he would do it so it is harsh.
“Obviously he is very family-orientated and he has never really been away before. But it is England and you can get from one place to another. It isn’t impossible these days. It is not to say that he is playing in Saudi Arabia.”
O’Neill paid tribute to his charges standing firm in the face after seeing his team dominated by Swansea.
“It was a difficult afternoon for us. Swansea are a very fine footballing side and they came here with plenty of confidence,” O’Neill added.
“They caused us problems in terms of possession but the win for us was the most important issue and two great goals decided the game.
"I am delighted with the determination the team have shown. I think that everything caught up with us today in terms of the amount of matches and the intensity of those matches.
"Deep down for all their possession Swansea had, they had a great chance before we scored and a free-kick that caused us a problem but other than that we were pretty resolute.”
How do you stay up to date with football when on the move? With http://m.goal.com – your best source for mobile coverage of the beautiful game