The Manchester United star has been linked with a move away from Old Trafford this summer, three years after rejoining the club from Juventus.
The Serie A champions have been mentioned as a possible destination for the Franceinternational, while Madrid have made the midfielder their top transfer target.
Zidane's side are looking to rebuild after a disastrous 2018-19 campaign that saw them finish well off the pace of Liga champions Barcelona.
Eden Hazard, Luka Jovic, Eder Militao, Ferland Mendy and Rodrygo have already been brought in after a season that also saw the Blancos fall to Ajax in the Champions League round of 16.
When asked about Pogba's possible arrival, the former France international gave a strong indication his side could be looking to continue their spending spree by bringing the 26-year-old to the Bernabeu.
"We need to respect everybody, but the only thing I can say from the club is we know what we want to do," Zidane said.
"Something could happen before the end of August. We could have some changes."
Pogba himself has said that he could be looking for a move away from Old Trafford, saying last month : "I think for me, it can be a good time to have a new challenge somewhere else."
The player's agent Mino Raiola also added fuel to the fire, saying that he is " in the process " of securing Pogba a transfer away from his current side.
For his part, Manchester United manager Ole Gunnar Solskjaer has said he is planning on keeping Pogba, having used the midfielder in his side's recent friendlies against Perth Glory, Leeds United and Inter.
"I can give him a new challenge," Solskjaer said of Pogba earlier this week.
Pogba is expected to be involved again as United continue their pre-season preparations on Thursday against Premier League rivals Tottenham.
United will have to make do with Europa League football this coming season, having finished in sixth place in the Premier League table in 2018-19.