The 25-year-old Everton midfielder has not played for his country since instigating a self-imposed exile in the wake of a disappointing Euro 2012 finals campaign, in which he did not get a chance to show what he could do.
However, assistant manager Marco Tardelli revealed Giovanni Trapattoni had contacted Gibson on Monday following David Meyler's withdrawal from the squad for Wednesday night's friendly against Poland with a knee injury.
While the answer came back in the negative, Tardelli insisted it did so because of his own fitness concerns rather than a desire not to return.
He said: "This morning, Meyler told us that he was going back home and we spoke with Darron and he told us that he has played just one match and he would prefer to stay at home because he is not available.
"He has a little problem after the match. I think Darron wanted to come here with us. The next match, maybe yes.
"He said, 'I have a little problem'. He is not available for this match. He was in Malaga because there is a little training camp with Everton.
"It's no problem to come for another match."
Asked if Gibson would be considered for selection for the trip to Sweden on March 22 and the home clash with Austria four days later, Tardelli said: "Yes, why not?
"Always when we need a player and the player wants to come with the Irish team, we are very happy.
"I don't understand why this problem exists. It's not my problem, it's not Gibson's problem."
Gibson was named in the squad for the Republic's first qualifier of the current campaign in Kazakhstan in September last year, but withdrew after telling Trapattoni the disappointment of what happened in Poland during the summer, and in particular his lack of a role in it, was still having an effect on him.
There has been dialogue between the two parties since with the 73-year-old Italian identifying the former Manchester United player as one of the men he felt could give his team a different focus in the immediate aftermath of the Euros.
Whether the call comes and is accepted next month remains to be seen, but in the meantime, Trapattoni will cast an eye over a series of new players on Wednesday with uncapped Derby trio Richard Keogh, Jeff Hendrick and Conor Sammon in the squad.
However, it is the goalkeeping position which could prove the most interesting with Trapattoni having voiced his displeasure with number one Keiren Westwood's lack of first-team football at Sunderland to the extent of suggesting he needs to leave Wearside to preserve his international career.
Millwall's David Forde is likely to get the nod against the Poles, and Tardelli has revealed he and Trapattoni would have no concerns about the 33-year-old starting against Sweden.
He said: "Forde is a good goalkeeper. He played against Italy and to play against Italy is very hard, and he played very well.
"He has big experience and I don't worry about him. I worry about Westwood because he doesn't play in his team, but not Forde."
Asked about Trapattoni telling Westwood he may need to leave Sunderland, Tardelli said: "He tried, but [Black Cats manager Martin] O'Neill decided that it was better that he stayed at Sunderland, and Giovanni can't do anything about that.
"For me, it would have been better if he had moved."
Shay Given, who won 125 caps for Ireland before announcing his retirement from international football after the Euros, has offered to return, but that option is yet to be taken up.
Tardelli said: "We know Shay Given loves to play with us and this is very important because other players, maybe they don't love to play for the Irish team.
"This is very important. If we need him, maybe it's possible."
The Football Association of Ireland later confirmed Leeds midfielder Paul Green has been drafted into the squad following Meyler's withdrawal.
Green will link up with the squad in Portmarnock in time to take part in
training at Gannon Park on Tuesday morning.