The England international scored his first Premier League goal for Liverpool in a 4-0 drubbing of Fulham at Anfield on Saturday, some 17 months after joining for a reported 20 million pounds in July 2011.
Downing, who also created the second goal with a fine through ball for Steven Gerrard, has failed to live up to expectations with some inconsistent displays but Rodgers hopes the 28-year-old has turned a corner.
"I spoke to Stewart about six or seven weeks ago and we had an honest conversation about where he was at. He's in his late 20s, he was an England international a few years ago and he wasn't playing [regularly for Liverpool]," Rodgers told the Liverpool website.
"So we spoke about how he could get into the team. And I think his reaction from that moment, like it has been for Jose Enrique and one or two of the others, has been outstanding."
There has been British media speculation that Downing, utilised at left back in some games this season, could be allowed to leave in the January transfer window but Rodgers said he was firmly part of his plans to build a side capable of getting back amongst the elite of English soccer.
"Stewart has played a lot of games. He's a very important member of our group at the minute and if he keeps performing like that, hopefully he'll establish himself in [the side] and show the talent he clearly has," he said.
"If he keeps playing like that, he'll be going nowhere - he'll be staying in the team and that's what it's about."
Liverpool's win over Fulham propelled them up to eighth place and to within five points of third-placed Arsenal.
Rodgers, in his first season at Anfield, said Liverpool were "improving steadily".
"You can see the confidence in the team," he added.
"If you lose like we did last week and then you come back to Anfield and play like we did today, it shows the courage of the players.
"If we keep making the progress that we have, then it should be a really exciting second half to the season for us."
The five-times European champions take on Zenit St Petersburg in the Europa League last 32 in February.
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