The midfielder boosted his chances after scoring the winner in the 1-0 Europa League victory over Anzhi Makhachkala on Thursday night.
While Rodgers resisted the temptation to rest a host of players for Sunday's Barclays Premier League trip to local rivals Everton and fielded a strong side against big-spending Russian outfit Anzhi, it was in fact one of the three men who came into the first XI who ultimately made the most telling contribution.
That was Downing, who having been shifted from the wing to full-back for the second half, cut in from the left flank in the 53rd minute and fired an unstoppable shot into the net from outside the area.
It was just the fourth goal of what has been a generally frustrating period for the 28-year-old England international following his move from Aston Villa in 2011, which has only grown more so since Rodgers succeeded Kenny Dalglish as Reds boss over the summer.
This season Downing has made only one Premier League start and the last time he played at all in the top flight was mid-September, but he is optimistic he may have put himself in contention to feature at Goodison Park with his efforts in the Anzhi win, which saw Liverpool move into top spot in Group A.
"It was satisfying to get the goal but the win was the most important thing," said Downing, quoted in the Liverpool Echo.
"The only way you can prove yourself to the manager is out on the field. All I can do is score goals and try to play well.
"I want to be playing in the Premier League and I'd love to play in the derby. Hopefully I've given the manager food for thought.
"We've got a big squad and the lads have done well recently so I'm not sure if the manager will change things.
"But I'm ready and waiting for a chance and when it comes I have to make sure I take it."
Downing took up the left-back position after Glen Johnson was substituted at the interval for Raheem Sterling.
"I enjoyed it at left-back - I've played there before," added Downing.
"Glen was struggling a bit at half-time and the manager didn't want to risk him. I went there no problem and that's where I got the goal from.
"I don't think I've scored many better than that. That was a good one and I was very happy with it."