Soldado, 30, has endured a torrid time since moving to White Hart Lane in 2013 and Sky sources reported earlier this summer that he was one of several players the club had put up for sale.
Spurs boss Mauricio Pochettino recently insisted that the Spain international was still in his plans, but Soldado has also been pictured on social media at Gatwick Airport on Thursday and reports in Spain believe he is set to join Villarreal.
Pochettino confirmed in his press conference that the striker is in Spain but refused to reveal any mroe details.
He said: “It is true the club have given permission for him to go to Spain, but the club will announce if something happens.”
Earlier, Lamela tweeted, before deleting: “I enjoyed these two years that we shared, I wish you well in your new club. Good luck my friend!”
Soldado, who was prolific in Spain for former club Valencia for many years, was part of the recruitment drive of 2013 that saw Spurs spend over £110m on seven players, before Gareth Bale moved to Real Madrid.
But he has struggled, scoring just seven Premier League goals in two years and 16 in all competitions altogether.
Tottenham are also close to bringing in a new striker in Lyon’s 21-year-old Clinton N’Jie.
The French club’s president confirmed on Wednesday that a deal had been verbally agreed between the two clubs.