Spurs chairman Daniel Levy has been in talks to sign the Cameroon striker, but Lyon are hoping to find a replacement before allowing Njie to depart.
“We are close to an agreement but there’s no urgency for us,” Aulas said.
“We want to complete our own signings first, but I thank Daniel Levy has made an offer that we now regard as consistent.
Lyon, who will return to the Champions League after a three-year absence, are hoping to sign a central defender and a midfielder by the end of the transfer window.
According to media reports, Tottenham are ready to pay around £10m plus up to £3m more in further payments for the 21-year-old.
Njie, who can play in several attacking positions, scored seven goals in 30 Ligue 1 appearances with Lyon last season.
Tottenham are in need of extra firepower to assist England striker Harry Kane as both Togo’s Emmanuel Adebayor and Spanish forward Roberto Soldado are likely to be allowed to leave White Hart Lane.