Khan emphasised Pacquiao has "signed" for the fight, though he was uncertain how things may play out if Thurman were to pursue any rematch with Pacquiao in the event he loses his WBA super-welterweight title on Saturday.
The eight-division boxing champion, an adopted son of Bacolod, and the unbeaten American will clash for the World Boxing Association (WBA) super welterweight title at the MGM Grand Garden Arena in Las Vegas, Nevada.
Khan won the WBC worldwide welterweight title with a fourth round stoppage of Australian Billy Dib in Jeddah on Friday.
"To have him sign that dotted line is brilliant".
"Hopefully it could be the Manny Pacquiao fight, we have both signed and the fight is done and hopefully he gets past his fight on the weekend then we go and do that fight". As far as I know it hasn't been even discussed. We wish him lots of success and hope to see him win more matches in the future. That is why I want to fight him.
Sternberg also said he did not know what prompted the Briton to make the claims.
The 32-year-old fought as recently as July 12, defeating Billy Dib in four rounds in King Abdullah Sports City, Jeddah, Saudi Arabia during an exhibition fight, where he is believed to have earned millions for the spectacle.
Khan was slated to fight Pacquiao, one of the sport's most decorated fighters, two years ago in the United Arab Emirates.
Same with his previous fights, Pacquiao is just letting his next opponent talk and once again, vows to let his fists do the talking. The Filipino is yet to publicly announce any meeting with Khan and has instead used his social media channels to focus on Saturday's fight with Thurman - who is undefeated in 29 outings. I have probably sparred between 200 and 300 rounds with him.
Khan has long courted a fight with multi-weight world champion Pacquiao, who will face Thurman this weekend having revived his career with victories over Lucas Matthysse and Adrien Broner following a shock loss to Jeff Horn in 2017.