The Aviva Premiership side get their Pool 1 campaign underway on Sunday when they entertain Italian outfit Rovigo.
Despite the league remaining their top priority this term, Skivington is hoping that the club can make their mark in Europe.
"Players, coaches, the club as a whole are ambitious and European rugby is exciting," he is quoted as saying by Premiershiprugby.com. "You lose a couple of games and you are out, you win a couple and you can get that momentum and end up flying through.
"The club has big plans and everything we approach we are going to attack. I'm not sure of the tactical plan but the club are certainly taking it very seriously and we will be hoping to do well."
London Irish are currently in ninth place in the Aviva Premiership table after taking 12 points from their opening six games of the season.