The 28-year-old Slovakia international lost his regular first-team spot to Jamie Carragher, who is retiring at the end of the season, after January's shock FA Cup defeat at Oldham.
He has started just one Premier League match since then - last month's 3-1 loss at Southampton, when Carragher was injured.
Rodgers has been heavily linked with a summer move for Wales captain and centre-back Ashley Williams, with whom he worked at former club Swansea.
That would put more pressure on Skrtel but he 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."