The Southampton striker hasn't played for over a year, but has committed to staying at the club despite reported interest from Tottenham, Liverpool and Manchester City.
In his press conference ahead of this weekend's game with Aston Villa, the Dutchman said that the target is for the forward to be among the substitutes when the Saints face Manchester City at the Etihad on the last day of the Premier League campaign.
"Jay is close," Koeman is quoted as saying by the BBC. "He's doing all the exercises with the team this week. If we can put him on the bench in the last game it will be a great achievement for Jay for what he did in coming back."
It would be a great story for Rodriguez to return against City, given that it was the same fixture the striker was injured in last season.
The cruciate ligament blow has caused the 25-year-old to miss the entire season so far, and Rodriguez was also in the running for a World Cup role with the England before his injury.
Despite not featuring for the Saints, he has been constantly linked with a switch to join up with former Southampton manager Mauricio Pochettino at Tottenham, while City themselves have also been said to have had an interest in the former Burnley man, according to the likes of the Mirror.
However, Rodriguez signed a new contract this week, keeping him at St Mary's for the next four years, meaning the forward can now concentrate solely on building up his match fitness and, hopefully, make the bench on May 24.