A report in Sunday's Gazzetta dello Sport newspaper claimed Juve had made "significant progress" in their bid to sign Drogba, who the report claimed has agreed in principle to an 18-month deal.
The 34-year-old signed a two-and-a-half-year contract with Shanghai Shenhua in July but the Ivory Coast international could be reconsidering his options after a disappointing start to his career in China.
However Conte insists Juventus - as well as other major clubs in Italy - are in no financial position to sign top players.
Speaking after the 3-0 win over Atalanta on Sunday which extended Juve's lead at the top of Serie A to seven points, Conte said: "Transfer talk seems disrespectful to the players in my team, especially at the current moment.
"It's a critical time as far as the economy is concerned and it's the same for several other teams.
"We won't be signing any top players because we're not in a position to. Neither us, nor other top teams in the Italian league."