The 32-year-old’s current contract is set to expire in the summer.
Coyle said: “We’ve put an offer to Ricardo and we’ll see what happens.
“He had a difficult season with injury but he came back and showed he wanted to be part of what we’re doing.
“It’s up to him. If he wants to sign, brilliant. If not, we’ll move on.”
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Liverpool have unveiled their new home kit for next season, sticking with the hugely popular retro styling of the current shirt.
The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.