Cordner has been limited to just 30 games for the Roosters over the past two years due to knee and pec injuries, with the former also impacting his ability to train at full capacity
As the current NSW Origin and Roosters co-captain Cordner is one of the biggest names off-contract in 2018, with Angus Chrichton's scheduled arrival from the Rabbitohs next season fuelling speculation that Cordner may have been on the outer.
NRL.com understands that Cordner's preference is to remain in the red, white and blue, and the final terms of a new extension will be thrashed out between the club and his management over the next fortnight.
The 25-year-old returned to pre-season training in the new year having undergone a stem-cell injection to regenerate the knee injury that limited him to 18 games last season.
Despite reported interest from the Knights, where good mates Mitchell Pearce and Aidan Guerra have landed, Robinson declared his confidence of locking in his skipper's services by the club's first pre-season trial against Penrith on February 17.
"I know we're pretty close with Boyd," Robinson told Sky Sports Radio on Friday morning.
"Hopefully there will be a response in the next couple of weeks."
Asked if he is confident of retaining the 16-Test international, Robinson responded: "I'd like to think so with Boyd being our captain and being here since he was a kid.
"We definitely want to see him stay here so hopefully that'll get done by the trials."
Cordner has previously attracted attention from his junior club Newcastle when he was last off-contract at the start of 2016, with Manly also chasing the gun back-rower before he inked his current two-year deal.
He has since been elevated to the club captaincy alongside Jake Friend, and played 126 games for the outfit he first joined as a 16-year-old.
Robinson also hinted the Roosters may still go to market again before the Telstra Premiership kicks off and add to the recruitment spree that has netted Cooper Cronk and James Tedesco for 2018.
With Pearce and Michael Gordon (Titans) exiting as a result of Robinson's cash splash, the Roosters have entered the new year with two free spots remaining in their top 30 squad.
One of those spots can remain vacant until June 30 under the NRL's new revised squad rules, but the other must be filled by March 1. The Tricolours' season kicks off against Tedesco's old side Wests Tigers on March 10.
With the departures of Guerra, Kane Evans, Liam Knight and Paul Carter from the Roosters forward stocks, a big body up front looms as the most likely addition with either the club's reserve grade ranks or another recruit to fill the void.
"Obviously with Mitchell going and Mick Gordon going to the Gold Coast that has left us with a couple of spots in our 30," Robinson said.
"I think you've got to fill 29 of them by the start of March and then you're allowed to leave one throughout the year.
"So we've let a couple of spots there mainly to see what the guys in reserve grade, see how they develop, so hopefully they might take one of those spots.
"Or we might recruit into those spots as well. So we've got a couple of spots up our sleeve with that different system that's quite interesting."