Zidane returned to the Bernabeu after only six months away earlier this week, replacing Santi Solari after a horrible season so far for Los Blancos.
Madrid have suffered after not replacing the Juventus-bound Cristiano Ronaldo last summer, and Zidane will likely have the funds to make significant additions.
According to The Mirror, Sterling may be among the targets in a "£300m-plus spree" alongside Christian Eriksen, Eden Hazard and Neymar.
The England forward is enjoying another terrific season for Manchester City as they gun for the title and Champions League, having netted 19 goals and supplied another 11 assists in all competitions.
Zidane has publicly declared his interest in the past, saying in 2015: "Of course we are monitoring him as a player."
It would take a huge sum to prise Sterling away from Manchester – he only signed a contract to 2023 last year, and City are not in a financial position whereby they need to sell players.
Zidane faces his first test as Madrid boss on Saturday afternoon against Celta Vigo.
'I think everybody has said something about it, so why should I add to it? It's so obvious that it's not necessary for me to' Everything that Liverpool boss Arne Slot said about James Tarkowski's unpunished horror tackle
Gary Lineker unveiled as FourFourTwo's latest cover star - we sat down with the legend of football and broadcasting to discuss his future after BBC Match of the Day
