Chelsea the favourites to get their man although suggestions of a £25m deal having been struck appear slightly off target.
Oscar's agent, Carlos Meinberg, told Brazilian paper Terra: "Chelsea did offer €25m (£19.8m) but there is still no agreement between the clubs.
"That may happen in the next few days. Oscar's other agent, Giuliano Bertolucci, will travel to England to finalise the remaining details.
"Tottenham also made an offer, but he should accept Chelsea's offer as there is more exposure there."