The Icelander was reported to be the person who allegedly leaked the Cardiff City team to Crystal Palace sporting director Iain Moody ahead of the match between the two sides
The Premier League are investigating the Welsh club's claim that Palace were made aware of their line-up well in advance of the top-flight clash at the Cardiff City Stadium earlier this month.
Midfielder Gunnarsson was reported to be the source of the information that was passed on ahead of Palace's 3-0 victory over Solskjaer's side.
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But Solskjaer has given his complete backing to the former Coventry City man and the 24-year-old is set to feature in Saturday's clash with Stoke City.
He said at a press conference on Friday: "We, as a club, will defend Aron's name and reputation to the hilt, I have complete faith in Aron as a player and as a man, as does the rest of the squad and staff.
"He will be involved in my squad for tomorrow's game at home to Stoke City and remains integral to what we are trying to achieve.
"Unfounded speculation regarding Aron's loyalty or commitment ends here, with focus returning to the important matters in hand on the field."
Goalkeeper David Marshall echoed his manager's sentiments and revealed that the episode has only succeeded in making relegation-threatened Cardiff even more motivated to stay up.
"Aron would never do anything to hurt this football club or squad – it's not the way he is and I know him well," the Scot added.
"He's one of the most honest and hard-working people I've ever met in football and the whole dressing room backs and trusts him 100 per cent.
"I'd put my life on Aron's integrity. We've rallied around him and the situation has brought the dressing room even closer. It makes us even more determined to succeed."