Dutch ace Kuyt is known to be a summer target for German side Hamburg, while Italian outfit Roma claim Israeli international Benayoun will be joining them later this month.
But Benitez has revealed that he has met with both players this week and insists that the duo will play a part in his plans for the forthcoming campaign.
Speaking to the club’s website, the Reds boss said: “Neither of them will be leaving.
“I have no more news about Yossi – he will be staying. I am really pleased with Kuyt. He will be staying.”
Benitez added: “I have talked to Yossi and told him I want to keep him. He is a player with quality and has shown that during pre-season.
“I also talked with Dirk Kuyt this morning. I am really pleased with him.”
Norwich midfielder James Maddison is being linked with a switch to Tottenham during the close season.
Manchester City are hoping to tie Raheem Sterling down to a new contract following reports Real Madrid are lining up a swoop.
Everton are in the hunt to sign Norwich midfielder James Maddison but will have to pay out £25million to have any chance.
Chelsea remain in the hunt to sign Arturo Vidal from Bayern Munich, but will face strong competition for his services.
Huddersfield Town Academy Manager Leigh Bromby admits getting youngsters into the first team is something the club can work on.
Watford's hopes of signing Bologna midfielder Simone Verdi could be hampered by interest from Leicester.