Interest in his services has built steadily after seeing the 25-year-old enter the final 12 months of his contract in Italy.
De Vrij, though, has hinted that an extension could soon be put in place, forcing the likes of Liverpool to look elsewhere in January and beyond.
“You never know what will happen, but my intention is to grow, improve and make the best decision for my career.”
Lazio are reported to have put an offer on the table which will keep De Vrij in Rome until 2020.
They remain determined to push that agreement through, with the club having moved to curb the ongoing transfer rumours.
Sporting director Igli Tare told reporters in September: “We are optimistic on De Vrij's contract renewal.
“We have a great understanding with his entourage.”
De Vrij has been with Lazio since moving to Italy from Feyenoord in 2014.