Everton were confident negotiations were advancing towards a successful conclusion on a three-year deal of their own for Tete.
Manager David Moyes has made full-back one of his summer priorities after 39-year-old Ashley Young was not offered a new contract, despite veteran captain Seamus Coleman signing a one-year deal to take him into a 17th season at the club.
Tete had emerged as Everton’s main target, but Moyes may now be forced to turn to alternatives that could include free agent Kyle Walker-Peters or his former right-back at West Ham, Vladimir Coufal.
Jake O’Brien, who was signed from Lyon as a central defender, performed consistently at right-back for Everton following Moyes’ appointment in January, having been ignored by predecessor Sean Dyche, while Scotland defender Nathan Patterson has also been used.