The Slovakia international lost his first-team spot to veteran Jamie Carragher, who is retiring at the end of the season, after January's FA Cup exit to League One Oldham.
He has started just one Premier League match - against Southampton when Carragher was injured - and has featured only three times since then.
Rodgers has been heavily linked with a move for Wales captain and centre-back Ashley Williams, with whom he worked at former club Swansea, in the summer.
That would put more pressure on Skrtel but the 28-year-old is determined to stand his ground.
"This is what happens in football and this time it was my turn," he told his official website, martin-skrtel.com.
"I have to respect it and wait for my chance and I hope my chance will come before the end of the season.
"Those who know me know that I will fight for my place in the team."