The duo have been relegated to training with the reserves.
Warnock was part of England's World Cup squad last summer but is now third-choice left-back behind Ciaran Clark and Nathan Baker. He had been linked with a loan move to his former club Liverpool last month but it failed to materialise.
Beye has not been part of Houllier's plans for nearly three months.
Houllier clearly wants the pair to show the right attitude if they are to return to the first-team fold and told the Birmingham Mail: "They must show the trust first and they must show they like the club. They're here, they're Aston Villa players, they are training with the reserves. If needed, they will fill in. If not, they won't.
"It's not only a matter of being good enough, it's also a matter of being committed enough. They're training with the reserves and they have to give their best because the reserves work hard. There's no point just being in our warm-downs, so they train with the reserves."
Source: PA
Source: PA