Venezuela international Feltscher, 29, joined the Bluebirds on a short-term contract last month.
It expires on January 13 and he is already eyeing up a move to the MLS.
According to The Sun on Sunday, Feltscher is expected to join LA Galaxy.
Feltscher is yet to feature for Cardiff, who are second in the Championship table.
He is reportedly unhappy with boss Neil Warnock at his lack of action.
After signing Feltscher, Warnock indicated that it would be nothing more than a short-term arrangement.
“He’s only here for seven weeks, I said I’d have to look at him, they wanted a couple of years, but I wasn’t able to do that so he came back and agreed,” the Cardiff gaffer said.
“He’s quite an attacking player, a little rash at times, but we’re going to have a look at him.
“Harry (Redknapp) told me about him originally because he was going to sign him and at that stage we had so many full-backs that we couldn’t do anything, but we liked what we saw.
“When he came back and said he wanted to try to impress us until January we said ‘alright, then’. I don’t want anything permanent at the moment, and he knows that, but it’s up to him now.”