The Englishman has attracted plenty of praise since arriving at Selhurst Park from Chelsea in the summer, leading to questions over whether the Eagles will be able to keep him in the long term.
The French manager has played down rumours though, telling Sky Sports: "It's too early to talk about this kind of decision, we are really glad he decided to come to our football club."
Vieira spoke highly of the loanee, saying: "It's a joy because his a player who wants to learn, he is prepared to work hard. The staff, myself, we are really enjoying working with him."
After he spent last season with West Bromwich Albion, Chelsea again loaned out the 21-year-old this term, and Gallagher is said to have taken well to life at Selhurst Park.
The midfielder has started in every league game this season other than the opening-day clash with his parent club, and he opened his account for the Eagles with a brace to help them come from behind to draw 2-2 away at West Ham United in August. body check tags ::