I consider Warren Buffett as one of the greatest investors the world has ever seen. He has shown a love and preference for American companies over his lifetime, but I think there are a few ASX shares he'd definitely want to own if he hunted here.

There are a number of traits that the investing legend looks for, such as a good valuation, honest and hardworking management, appealing potential to put more money to work within the business at a high rate of return, and that these businesses are in industries he understands.

A lot of share prices have risen recently, so it's a bit harder to find value. However, Buffett has said a number of times that he would rather buy a wonderful business at a fair price rather than a fair business at a wonderful price.

Below are the three ASX shares I think Warren Buffett would love to own.

Premier Investments is an ASX retail share that owns a number of brands including Smiggle, Portmans, Just Jeans, Peter Alexander, Jay Jays, Jacqui E and Dotti.

The company also owns investments in two other ASX companies – Breville Group Ltd (ASX: BRG) and Myer Holdings Ltd (ASX: MYR).

The two brands I really like within the portfolio are Smiggle and Peter Alexander.

Smiggle sells school-related items such as lunchboxes, drink bottles, bags, stationery and so on. Some of the current brands it's working with include Jurassic Park, AFL, Spider-Man, Minecraft, Barbie and Mickey and Minnie.

Now that the COVID-19 impacts on schools have dissipated, the growth potential of Smiggle has returned to normal.  

The company is planning a lot of international growth for Smiggle and Peter Alexander. I think store growth can be a big driver of earnings in the coming years, so the company has a promising outlook, in my opinion. Smiggle can expand in numerous countries.

A bonus could be if the business' strategic review manages to unlock value for shareholders.

According to Commsec, the Premier Investments share price is valued at 24 times FY24's estimated earnings.

Beacon Lighting is best known for its stores across Australia, which has tailwinds like population growth in Australia. Any interest rate cuts this year could be a boost for demand.

One the things that excites me most about this business is its international growth. Australia is a great country, but the global population is much bigger – tapping into this addressable market is compelling. It has offices in Hong Kong, mainland China, the USA and Germany. In 2023 it made sales to customers from 45 countries.

It's looking to build trade and commercial partnerships, growing its sales to business customers. The ASX share would also like to expand its store network and grow its e-commerce sales.

According to the projection on Commsec, the Beacon Lighting share price is valued at 20 times FY24's estimated earnings.

Wesfarmers owns a number of Australis's leading retailers including Bunnings, Kmart and Officeworks. Other businesses it operates include Target, Catch and Priceline.

I think Warren Buffett would definitely want a piece of Wesfarmers. The company has proven to be a long-term performer, with a track record of making good decisions for shareholders and generating a good return on equity (ROE).

Berkshire Hathaway has built up a diversified portfolio of businesses, and Wesfarmers is diversified too. Wesfarmers is expanding into areas like healthcare and lithium. The more growth avenues the company has, the more choices it has to invest in the best-returning option.  

According to the estimate on Commsec, the Wesfarmers share price is valued at 30 times FY24's estimated earnings.