The 23-year-old, who joined in 2011, failed to make a single Premier League appearance last season as a knee injury kept him sidelined, before returning on loan to former club Nacional in January.
Coates is yet to truly establish himself on Merseyside and has featured just 24 times in all competitions during his three-year stay with the Reds.
The Uruguay international has been linked with a departure this summer following the arrival of Dejan Lovren from Southampton, but he plans on fighting for a place in the side despite the increased competition in defence.
"Last season was really difficult. I had a bad injury and after being out for so long, it's great to be back fit," he told the Liverpool Echo.
"I try always to give my best and I know I need to improve more on the other years that I've been in England.
"The manager is watching me closely - like he is with all the other players - and I need to keep performing well.
"I would like to stay at Liverpool and play, but that doesn't depend only on me. It depends on the manager and the club.
"They will decide what happens. After being out for so long, I need to play. If I do stay I want to play more than I did in the other years."
Uruguay team-mate Luis Suarez has already exited the club to join Barcelona this summer, but Coates insists that move will have no bearing on his own future.
"Just because Luis has gone, that doesn't mean that I want to go," he said.
"He's a different player and a different person. I must take care of my own future."