The club's leading goal scorer this season was expected to be ruled out for a month, but a quicker-than-expected recovery from a hernia operation could see him feature on Saturday
Hull manager Steve Bruce has hailed Brady's speedy rehabilitation as "incredible" as he prepares to welcome the 21-year-old back into his plans for the trip to Goodison Park just a matter of weeks after he went under the knife.
Brady is the side's leading scorer in the Premier League this season with three goals in six appearances, including one in his last outing when Hull beat West Ham 1-0 at the end of last month.
The return to fitness of the Republic of Ireland international is a timely boost for Bruce.
"We'll see how he is and how he trains and hopefully he'll be OK," Bruce told the club's official website.
"With modern medicine, it's quite incredible that you can be back playing within two or three weeks and we expect him to take some part [against Everton]."
Hull head to Merseyside striving to extend a five-match unbeaten run that has seen the side progress to the League Cup fourth round and sit eighth in the Premier League, above the likes of Manchester United.