The Juventus striker has attracted interest from across Europe this summer.
The fee is reportedly deemed adequate by the Italian champions but Spurs still have their work cut out to get a deal over the line.
The Spaniard has been linked with West Ham and Monaco, by the likes of La Gazzetta dello Sport, but Porto appear to be Spurs' biggest rivals for his signature and Sportmediaset claims Llorente favours a move to the Portuguese club.
Tottenham's latest offer is thought to be higher than Porto’s and it remains to be seen whether last season's Primeira Liga runners-up will increase their bid.
At 30 years old and unproven in England, any move for Llorente represents a risk and a fee of over £10 million is a substantial one.
The Juventus striker has demonstrated his quality over the years however, and while his time in Italy hasn’t been the most productive, he still offers a real threat and would add useful variety to the Spurs attack.
He is unlikely to be the solution to Tottenham's attacking needs but given the possible departures of Roberto Soldado and Emmanuel Adebayor, Spurs will need a couple of attacking additions and Fernando Llorente is more than capable of being one of those.