Atkinson signed a new contract with the club in February and has played every minute at inside centre in 11 out of 13 Premiership matches so far.
Skivington said Atkinson was one of the “top three” names who would be picked out by his team-mates as key to the club’s strong performances this season.
Victory against the Bears moved Gloucester back into the top four, level on points with third-placed Leicester.
“He’s got brilliant power and it’s deceptive I think, he’s got a great skillset. He’s a brilliant individual,” Skivington said.
“He’s in the leadership group at his age already which says a lot, he takes this very seriously. He’s not here to mess around and get paid and go home, he’s here to win.
“Internally he’d be one of the top three names mentioned as to why things are going well at the club, if you asked the boys.”
Atkinson added it would “be nice” to be on the England radar but that club honours are his main focus.
“I’m just focussing on what we’re doing at Gloucester and pushing on to the end of the season and if that comes, it comes,” Atkinson said.
“I’m trying to find a balance of my game. I know that my passing game’s really strong but trying to find some carrying, breaking tackles, fighting the extra few metres to get us on the front foot is something I’ve been working on really hard this year and I was glad I could show that.”
