The 30-year-old U.S. screen star is around six months along in the pregnancy, according to the New York Post's gossip column Page Six.
"They're expecting a baby this winter," a source told the outlet.
While the child will be the first for Haley, Joe, 46, is already father to sons Zubin, seven, and Mohan, three, with ex-wife Anoushka Shankar.
The pregnancy rumours come just a month after Haley and Joe went public with their romance, with the blonde star sharing a picture of the pair kissing, which she captioned: "Cling to me, Joe, my bliss."
According to reports,the pair started dating at the beginning of the year - shortly after his split from Anoushka.
A representative for the director confirmed the break-up news in January, stating: "They ask that their privacy be respected."
Three days prior shattered Anoushka posted a message on Instagram which hinted at the separation.
"I said I loved you, and you heard me say you were not enough... you asked me to hold you tighter, and I heard you say I was not enough... how could we be enough for each other when we were never enough for ourselves?" she wrote.
Joe and Anoushka's divorce was granted in May, with his former wife, the half sister of singer Norah Jones, revealed her marriage had broken down following the English director's affair with an "unnamed woman".
The judge concluded that Joe had committed adultery.
Joe was previously engaged to actress Rosamund Pike. The pair met in 2005 on the set of film "Pride and Prejudice" and got engaged in 2008. They were due to marry that year, but Joe suddenly called off the wedding.