The 26-year-old has scored 11 goals and registered 10 assists for Spurs this term prior to Sunday's Premier League trip to Chelsea.
According to Spanish newspaper Don Balon, however, Barca talisman Messi does not want the club to pursue a deal for the Danish midfielder as a replacement for Andres Iniesta.
The report claims that the Argentine does not see Eriksen as Iniesta's successor and considers him to be too similar to Ivan Rakitic.
In addition, Messi reportedly believes that the January acquisition of Philippe Coutinho would also render the Spurs man surplus to requirements at Camp Nou.
A different report by El Gol Digital claims that Tottenham have already found an ideal replacement for Eriksen in Sporting Lisbon midfielder Bruno Fernandes.