Pogba was heavily linked with a move to the Bernabeu last summer after declaring in June that he wanted a "new challenge" following three mixed seasons at Manchester United.
Eriksen, meanwhile, was tipped to leave Tottenham Hotspur over the summer having failed to agree a new contract with the North London club, prompting Los Blancos to register their interest in the playmaker.
According to AS, however, the La Liga side will not move for either player in January after a heavy spending spree over the summer.
Having shelled out a total of £276.75m on recruits over the summer, Real president Florentino Perez has told Zinedine Zidane to work on accommodating the players signed in the previous window.
Madrid, who lost 1-0 to Mallorca in their last league game, will return to the top of La Liga if they beat Leganes on Wednesday.