Gibson began a self-imposed international exile following the disappointment of not featuring in last year's European Championships and was not named in Friday's squad for the crucial qualification double-header on March 22 in Stockholm and four days later in Dublin.
Aston Villa defender Richard Dunne is left out as he struggles to recover from a groin injury, but Everton's Seamus Coleman and Stoke's Marc Wilson have been included, as has Reading defender Stephen Kelly despite his public fall-out with Trapattoni in the aftermath of last month's 2-0 friendly win against Poland.
Trapattoni revealed he has spoken with Gibson but the 25-year-old is not yet ready to make his international return.
"I was in touch with him and he said that he is still not ready," Trapattoni told the Irish Times.
"I saw him in the last game and I told him that I was there but he said that he didn't want the controversy and he wanted to stay so I respect his decision."
When the Italian was asked if Gibson could return in the future, Trapattoni said: "Why not? He's a good player and I won't forget him."
Norwich's uncapped midfielder Anthony Pilkington is retained from the squad which faced Poland and West Brom's Shane Long is also included despite worries over an ankle injury.
Bolton midfielder Keith Andrews misses out due to an Achilles problem but Wilson is included despite only having played two games for Stoke in his comeback from four months out with a broken leg.
Speaking today in Dublin, Trapattoni said: "Last month's friendly game against Poland was a great opportunity to work with younger players, and I saw a lot of potential from them.
"We played very well during the game, and I intend on building from that performance this month.
"These two games against Sweden and Austria are very important, and we are focused on the task in hand.
"I am confident that these players can work together to produce the results we need. Sweden and Austria are two very strong teams, who have done very well in Group C to date.
"However, I believe that our players have the mentality and attitude necessary to qualify. I am looking forward to assembling the squad on March 17."