Arsenal and Spurs are set to be disappointed as a Serie A side are reportedly set to win the race for a midfield target.
Porto captain Herrera, 28, is out of contract in the summer, and has attracted the attention of several European clubs with no signs that he will pen a new deal.
Arsenal were understood to be among the leading contenders for his signature, while O Jogo speculated that Spanish giants Real Madrid had joined the race for the Mexico international.
Herrera will be available on a free transfer, and has been suggested as a potential replacement for Aaron Ramsey, who is expected to leave Arsenal in the summer when his own contract also expires.
However, the latest reports indicate that Arsenal will have a job on their hands if they are to land the vastly experienced Porto star.
According to Italian paper Il Corriere dello Sport, Roma could close a potential deal for Herrera in the January transfer window.
Club president James Pallotta has given the go-ahead to launch a winter assault for the 28-year-old, but they will not pay his €40m release clause due to his contract situation.
The report does confirm the interest of both north London clubs, though it insists that Roma are intent on beating competition from England to land Herrera.
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