The Anfield giants rejected an increased bid of £40,000,001 for the Uruguayan hitman from Arsenal earlier in the week.
And Downing is hoping the Gunners fail to meet their reported £55million valuation of the player in the hope that he stays on Merseyside.
"It's so important for us to keep hold of him as Luis is one hell of a player," said the 29-year-old, quoted in 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."
And the former Middlesbrough and Aston Villa man hopes manager Brendan Rogers and the club's hierarchy can convince Suarez to remain at the club as they look to challenge for a top four spot.
"Since he came back Luis has been training really well and I think whatever happens with his Liverpool future will be sorted out in the next week or two," he added.
"We want to keep our best players to help us get into the Champions League. That has to be our aim.
"We've strengthened the squad with new signings and I'm sure there will be a few more to come.
"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."