Joshua, 27, stopped Klitschko in the 11th round of Saturday's Wembley super-fight to add the vacant WBA and IBO titles to his IBF crown.
He has offered Klitschko a rematch and also has his eyes on an-all British clash with Tyson Fury, who has not fought since spectacularly dethroning Klitschko in November 2015.
"If it works out for my career, I'll definitely relish the challenge against Tyson Fury or anyone else for that matter," Joshua wrote in a column for the London Evening Standard newspaper published on Tuesday.
"The fans want the Fury fight and I do, too."
Fury, 28, has claimed he could beat Joshua "with one arm tied behind my back".
The self-proclaimed 'Gypsy King' has relinquished his titles and had his boxing licence revoked after revealing he is battling mental health problems.
On the prospect of fighting Fury, Joshua said "it feels that we're heading in that direction".
"If I have to go through everyone in the division, then great. I am not hearing, 'Let's see Fury v (Deontay) Wilder or Wilder v (Joshua) Parker.' It's always, 'We want AJ versus Wilder, Fury and Parker.'
"So if I have to go through the division to keep it entertaining, then that's what we'll do -- take them out one by one."
Joshua said his victory over Klitschko, in which he overcame a sixth-round knockdown, showed he "can knock anyone out".
Disclaimer: No Business Standard Journalist was involved in creation of this content
You’ve reached your limit of {{free_limit}} free articles this month.
Subscribe now for unlimited access.
Already subscribed? Log in
Subscribe to read the full story →
Smart Quarterly
₹900
3 Months
₹300/Month
Smart Essential
₹2,700
1 Year
₹225/Month
Super Saver
₹3,900
2 Years
₹162/Month
Renews automatically, cancel anytime
Here’s what’s included in our digital subscription plans
Exclusive premium stories online
Over 30 premium stories daily, handpicked by our editors


Complimentary Access to The New York Times
News, Games, Cooking, Audio, Wirecutter & The Athletic
Business Standard Epaper
Digital replica of our daily newspaper — with options to read, save, and share


Curated Newsletters
Insights on markets, finance, politics, tech, and more delivered to your inbox
Market Analysis & Investment Insights
In-depth market analysis & insights with access to The Smart Investor


Archives
Repository of articles and publications dating back to 1997
Ad-free Reading
Uninterrupted reading experience with no advertisements


Seamless Access Across All Devices
Access Business Standard across devices — mobile, tablet, or PC, via web or app
