The forward put himself on the map by scoring a fine goal for Australia against Türkiye at the World Cup last month, with Watford transfer chief Gian Luca Nani revealing he is being talked about all over the world.
The Watford Observer understands the Hornets have already turned down a £10m offer from newly-promoted Premier League side Hull City, with interest from within England and Italy known.
Nani could not guarantee Irankunda won’t be sold this summer – and the forward has suggested he is not far off being ready to take the next step in his career.
He told SBS Sport in Australia: “I see myself playing at a top level soon, whether that’s now or next season.
“It will happen eventually in my opinion. I have that belief in myself that I can get to that level one day.
“Time will tell.”
Irankunda scored four goals on his debut campaign at Vicarage Road last term, showing glimpses of superb individual potential particularly in the second half of the campaign.
His performances earned him a spot on the plane to USA, Canada and Mexico, where he followed in the footsteps of previous Australian legends by impressing on the biggest stage.
He said: “It’s a dream come true because I watched all the World Cups before this one and I was able to participate in this World Cup.
“When you see moments like Tim Cahill (vs the Netherlands in 2014) and Matthew Leckie’s goal against Denmark (in 2022), you want to do something like that.
“To be able to do that against Türkiye and see the reaction back home was an amazing feeling.
“It’s something that I want to continue doing, which is giving back to the people who show so much love to us South Australian boys and all the boys who play in the national team.”