The American, 53, is said to be keen to join the wave of US investment in England's top flight.
The interest comes as Spurs' current owner, British billionaire Joe Lewis, has been bailed amid criminal charges relating to insider trading in the US.
If found guilty, Lewis would be forced to give up ownership of the North London club as per the Premier League's rules.
Jay-Z, real name Shawn Corey Carter, is said to be "waiting in the wings" should Lewis lose his case in court.
The rapper has previously discussed his interest in investing in a Premier League club, with rumours linking him with an investment in Arsenal in recent times.
Speaking back in 2010, he said: "I don’t know a lot about the business of soccer, but in the future if the right opportunity presented itself, then who knows?
"I am a businessman, and I will always look at an opportunity, and if it feels right great."
Any deal - likely to consist of a group of investors - would include the ownership and potential naming rights for the Tottenham Hotspur Stadium, where Jay-Z's wife Beyonce recently played a host of sold-out shows.
"More than a few of the very top clubs there – like Manchester United, Liverpool and Chelsea – are now under US ownership and Jay would jump at the chance of a controlling interest at board level somewhere with the global reach of Spurs," a business associate of Jay Z-told the Express.
"It remains to be seen whether Mr. Lewis will walk away free. If he doesn't, Jay has said he wants to be in a position to move quickly if he feels the price is right."
He is said to be worth around $2.5 billion (£1.95 billion) according to Forbes. In the past, he has been a major stakeholder in the NBA's Brooklyn Nets, and his Roc Nation Sports agency represents several high-profile athletes including Romelu Lukaku, Marcus Rashford and both Reece and Lauren James.
