With both being top quality midfielders and stars of their respective teams in the Premier League, neither will be cheap, meaning the La Liga giants can't sign both.
According to 'AS', Madrid are now weighing up which footballer to make a move for, looking at who would fit in better and considering their situations at their current clubs.
Both, for example, have admitted their desire to leave, with Pogba stating he wants a "new challenge" and Eriksen saying that going to Madrid would be a "step-up" in his career.
The two are similar ages (Pogba is 26 whilst Eriksen is 27), but they have very different styles of play. Pogba is more of a physical presence whose late runs into the box give him a goalscoring threat, whereas within the slighter figure of Eriksen is a midfielder who excels in picking out the final pass.
ZIdane is rumoured to favour a move for his fellow Frenchman, although Manchester United are reportedly unwilling to let go of their star this summer. Prising the Dane away from Tottenham could be a similarly difficult task, although the fact his contract is up next summer could give Real some room to bargain.
Madrid have already signed Eder Militao, Rodrygo, Eden Hazard, Luka Jovic and Ferland Mendy ahead of next season, and Pogba or Eriksen could be the next name on this star-studded list.