Coutinho scored two and created another as Liverpool thrashed the Hammers 4-0 at the London Stadium - a result which took them to the brink of Champions League qualification.
The 24-year-old has been linked with a move to Barcelona this summer, but Origi is hopeful that the Reds can keep hold of the "special" playmaker.
"He has moments of magic. I think he has a lot of talent and he's a top player and an experienced player and he's still only 24, so I think that's very special," the Belgian told the club's official website.
"He helps us a lot, is there in the big moments and for me he is a joy to play with. Daniel [Sturridge] as well is a big talent and of course he has experience. He showed his qualities again for Liverpool and he's very important."
Liverpool will secure a top-four spot with victory at home to relegated Middlesbrough on the final day of the season.