The Uruguayan continues to be linked with a £40million move to Arsenal but winger Downing has implored the club to do everything in their power to keep him at Anfield.
"It's so important for us to keep hold of him as Luis is one hell of a player," Downing told The Sun.
"He's had some good discussions with the manager which will remain private.
"For us as players nothing changes. He's still the same player and he's a great lad to have around the place.
"He gets on well with all the lads. Luis knows we all want him to stay. It'd be so disappointing to lose him."
Downing added: "If we can reproduce the form we showed in the second half of last season, we'll have a good chance of breaking into that top four.
"We want Luis to be part of that. He's a top player, one of the best in the world - we saw that with the goals he scored last season."