Receiving passive income from the ASX shares we've invested our hard-earned cash into is one of the most rewarding aspects of investing in the stock market. That tangible fruit of the labours of your capital can be used to pay bills, buy more shares, or, if you're so inclined, buy something nice for yourself.

So it goes without saying that I love receiving this passive income from my own shares. Indeed, many of my portfolio positions were purchased with the dividend income potential in mind.

But today, let's discuss two ASX passive income dividend shares that I don't yet own but would love to because of their income potential.

2 ASX shares I'd love to buy for big passive income

Coles Group Ltd (ASX: COL)

I've long admired Coles' dividend prowess. This company has paid a remarkably steady yet hefty dividend ever since listing on the ASX in 2018. In fact, this company has even managed to increase its annual dividends every single year since then. They also happen to come with full franking credits attached.

Coles' nature as a consumer staples stock enables the company to be a consistent provider of shareholder income. After all, we all continue to buy groceries and household essentials, regardless of the economy or stock market.

So we've established that this stock appeals to me as a dividend investment. However, I have yet to bite the bullet on buying Coles shares. It was only earlier this year that this passive income payer was in the $15-a-share range.

I regard today's ~$18 levels as a bit pricey for my liking. But if Coles drops back down to $16 or even $15 a share, and its dividend yield gets back over 4%, I'd happily add some stock to my passive income portfolio.

TechnologyOne Ltd (ASX: TNE)

Next up we have another ASX passive income share that I'd love to buy in tech stock TechnologyOne. This enterprise software provider has been dazzling ASX investors for years with its impressive growth numbers. But on the surface, it doesn't exactly look like a logical pick for that passive dividend income.

Over the past 12 months, TechnologyOne has doled out 16.98 cents per share in ordinary dividend income (there was also a special dividend last year, but we'll leave that aside for now). That 16.98 cents per share total gives this stock a trailing dividend yield of 0.7% at yesterday's closing share price of $24.14.

Now, 0.7% clearly won't give you much at all in the way of passive income right now. But I don't want to buy this stock for income today. I want to own it for the future income it could pay me.

TechnologyOne has been raising its dividends over the past few years, but its life depended on it. Yes, investors have seen 16.98 cents per share in dividends over the past year. But it was only back in 2019 that shareholders bagged just 11.9 cents per share. In 2015, it was 6.6 cents per share in total.

This company has also paid an annual dividend every year since 1996 – not a bad track record.

In 2023, TechnologyOne told investors that its final dividends over the previous ten years had grown at a compounded annual growth rate of 13% per annum. If this passive income growth continues into the future, that 0.7% yield won't stay static for long for shareholders. That's why I'd love to add TechnologyOne to my ASX dividend portfolio.