The 22-year-old winger, one of the stars of Wales' Six Nations success, is out of contract at the end of the season and is reportedly attracting the interest of big-spending clubs in France.
But Cuthbert, who rejected overtures from France before signing his current deal towards the end of last season, believes it is important young players remain in Wales, despite seeing his own region have a difficult start to the season.
He said: "I'm still developing and still have so much to learn. Being in the Wales environment helps a lot - working with Rob (Howley), Shaun (Edwards), Neil (Jenkins) and Warren (Gatland) is only going to further my development.
"The longer I'm in this environment, and the closer I am to it, is only going to be good for me."
And when asked if it was his preference to commit himself to the Blues, Cuthbert added: "Yeah, I think so. I will go with my own options but if I'm thinking like this, it would be (my first choice)."
Those words will be a major boost to Blues' chief executive Richard Holland, who had said keeping hold of the three-quarter was a priority.
Cuthbert said: "I'm still young, in only my second season, so I feel quite privileged to hear him to say something like that. I'm grateful to the Blues for giving me a chance. It's exciting times."
Cuthbert's Blues' colleague Jamie Roberts last week revealed he will leave the Arms Park at the end of the season, and is likely to join Wales squad members James Hook, Mike Phillips, Luke Charteris and Gethin Jenkins in plying his trade across the Channel.
Newport Gwent Dragons flanker Dan Lydiate and Ospreys fly-half Dan Biggar also reportedly closing in on moves to France.