Carlos Alcaraz defended his Wimbledon crown on Sunday while Spain won the Euros after beating England in the final a few hours later.
Fellow golfer and compatriot Sergio Garcia also lifted his first title in four years when he won the LIV Golf Andalucia event in a playoff and Rahm said it had been a great month for Spanish sports.
"A lot of history being done, with Alcaraz being the sixth player to win the French Open and Wimbledon in the same year and (winning) four Grand Slams at a very young age, Spain winning the fourth European championship," Rahm told reporters on Tuesday.
"And Sergio and his team doing what they did on Sunday, quite special. Coming back to a venue like this with so much history, it would be quite incredible to earn an Open Championship on this golf course in this tournament.
"It's arguably my favourite week in golf. And to maybe even continue this stretch of great Spanish sports, it would be absolutely fantastic."
The 152nd Open is being held at the Royal Troon Golf Club in Scotland and twice-major winner Rahm said he had noticed how the locals warmed up to him simply because he was from Spain, thanks to their defeat of rivals England in the final.
"Played all 18 holes yesterday and I think I got more congratulations for something that I didn't do than I ever have in my life," Rahm said amid laughter.
"I don't know what they've done, but anytime anybody plays against the English national team, every other country in Europe just unifies against them. I don't know why or what they've done, I'm not aware of the history.
"I think because we've heard (the song) 'It's Coming Home' so many times the last few years, that nobody wants to see it come home at this point."
Rahm said he was unable to watch Alcaraz beat Novak Djokovic in the Wimbledon final but did get updates from fans while out on the course.
He did, however, watch the EURO 2024 title decider alongside English golfer Tyrrell Hatton.
"The team was sharing a house that week, so me and Tyrrell watched it together. You can imagine that was a sight to see... Honestly, he's no different to any other football fan out there," he said.
"I've seen enough football with both Spanish and English supporters, and everybody's language is extremely colourful. So I would say he was right up the line of basically any other football fan that was watching that game.
"I think he knew, especially early on with how good Spain was playing, that it was going to be a tough match for England."
