Spurs reignited discussions with the French club this week regarding the acquisition of the 25-year-old, and are seemingly on the verge of striking a deal.
"We are close to Tottenham and the decision is now up to Hugo, who must have had a number of contacts with the English club," said Aulas on Lyon's official website.
"This transfer can be done at the end of the transfer window."
"Would it be better for us to see him leaving? Since we have an objective to reduce the wage bill, this transfer enters in our programme. But if he stays here, we will be very happy."
Lloris joined Lyon from Nice in 2008.