The 24-year-old has made more than 70 league appearances for the Lisbon giants - scoring 17 times - since graduating from the club's youth ranks.
Djalo has represented Portugal at under-19, 20, 21, 23 and B level since 2005, and was in contention for a place in Carlos Queiroz's senior squad for the World Cup finals.
And as a result, he has become the subject of interest from abroad, with both Spurs and Newcastle said to have expressed an interest in the forward's services.
"Sporting will let him leave for a fee in the region of €7-8 million," Djalo's representitive Lionel da Silva told Record.
"The offers we have in our hands, from Tottenham and Newcastle, are over the €5 million mark.
"Therefore, given the difference at stake, I believe this matter will be solved quickly. We have been much more distant before."
White Hart Lane chief Harry Redknapp is being linked with a string of frontmen - including Luis Suarez, Klaas-Jan Huntelaar and Luis Fabiano - as he attempts to bolster his squad ahead of Tottenham's first ever Champions League campaign.
With the futures of both Robbie Keane and Roman Pavlyuchenko uncertain, Redknapp will be keen to add at least one new face to his ranks ahead of Spurs' European qualifying ties at the beginning of August.
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