Khan, the British boxer of Pakistan origin, has expressed a desire to lock horns with Olympic bronze-medallist Vijender a number of times but the bout has not materialised yet.
During the announcement of his last bout, Khan had also claimed that Vijender was scared of him. Replying to his challenge, the Haryana-boxer said it was Khan who picked juniors to fight against.
"I am ready to fight with Amir. He picked a junior boxer to fight. Neeraj Goyat is way junior to me. I had said before and I am saying it again I am ready to fight whenever he tells me to. He should stop fighting kids," Vijender said on the sidelines of a felicitation event organised by Platinum Heavy Duty Cement.
A bout between the two prolific boxers may, however, be a long shot as Khan competes in the welterweight category (63.5kg-66.7kg) while Vijender contests in the super middleweight division (73kg-76kg) but the Indian was quick to come up with a solution for the problem.
"I can reduce my weight a little and he can increase it and we can agree on a mid point. He has done it before."
Vijender, who is still unbeaten in the professional arena, prevailed in his US debut against Mike Snider with a Technical Knockout to notch his 11th consecutive victory in the circuit.
Talking about his US debut and the bout, Vijender said America is the Mecca of boxing.
"America is so big, every opponent has some strength. They say everything starts and ends from the US. One of the best boxers work there.
"I had no idea about Mike before the bout. On the last day, my coach showed a video of him and how he fights. Earlier, I felt he is not such a good boxer but when his first punch connected me, I was shaken I felt yes now I am in the league."
Talking about his future plans, Vijender said his team is working on scheduling two bouts in the next 6-7 months where he might get a shot at prestigious titles.
"We plan to have two more fights. One around October-September and next in January-February. We are trying to work around the venue and opponent. The top boxers in US have a busy schedule," he said.
"America is a very mature market in boxing. Now the fights are going to get tougher and bigger. International or intercontinental titles might be coming up in 2020," Vijender's promoter Neerav Tomar said.
Asked if he regrets his tryst with politics owing to the loss from Delhi's South Delhi constituency in the Lok Sabha elections earlier this year, the multi-faceted boxer said he is open to accepting all opportunities life provides him.
"Galat faisale ko bhi jo sahi karde usko Vijender Singh kehte hain," he said.
"I never say no to anything. Life teaches you something everyday. I saw it as an opportunity to work for the people. I am thinking I will go to the moon, I never say no to anything. But I will never leave boxing because this is my identity."
The boxer also spoke about starting his own Boxing Club.
"I want boxing to become popular in the entire country so I am going to start a 'Boxing Club by Vijender Singh'. The youth gets easily distracted by drugs, crime etc so I think this is the right way to keep them on track.
"We will be starting from Delhi where there will be 150 young boxers and we will teach them the sport and provide all the equipment. I will visit the club once a month," Vijender said.