Downing scored his first league goal for the club and set up another in a 4-0 win on Saturday night - just a week after he admitted he could be leaving Anfield in January.
And Rodgers afterwards claimed he has never sought to sell a player who has divided opinion among supporters since a £20million move from Aston Villa in the summer of 2011.
He said: "Stewart's been brilliant, he's a real good guy. I want him to be a part of the group here but at his age, we talked about him playing regularly and if the opportunity had come for him to go then him and I would look at it.
"But the reaction from that conversation six or seven weeks ago has been outstanding. He's played a lot of games and I thought he was brilliant.
"If he keeps playing like that then he'll be in the team so there's no need for him to leave to get a game. I always have wanted him to stay. It's not about me pushing him out the door, he's a quality player."
Of his side's overall performance, Rodgers added: "We performed as well as that in a lot of the games to be honest but never always got the result. We were outstanding in every element of our game."