Coates has made just 12 Premier League appearances for Liverpool since arriving at the club from Nacional in 2011, with a serious knee injury forcing him to miss most of last season.
The 23-year-old Uruguay international spent the second half of the 2013-14 campaign on loan at former club Nacional.
Coates is now attempting to work his way into Brendan Rodgers' plans, starting three of Liverpool's four pre-season friendlies in the United States.
"Last season was really difficult. I had a bad injury and after being out for so long it's great to be back fit," Coates told the Liverpool Echo.
"I try always to give my best and I know I need to improve more on the others years that I've been here.
"The manager is watching me closely, like he is with all the other players, and I need to keep performing well.
"It's good for the club to have signed a player like [Dejan] Lovren and it's good for me to have that kind of competition as you always learn from playing with good players.
"I would like to stay at Liverpool and play but that's not just down to 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."
"Just because Luis has gone that doesn't mean that I want to go," Coates said.
"He's a different player and a different person. I must take care of my own future."
