Rodriguez has not featured since the 2-2 home draw with Leicester City in mid-October, after undergoing foot surgery.
However, he has been back in training recently and could feature when Technical Director Martin Hunter takes his under-21 side to the Foxes next week.
"Jay is more close,” Koeman told youtube.com/southamptonfc
when asked about the status of Rodriguez and fellow long-term absentee Florin Gardos, who is working his way back from a knee injury.
“He did not do the session this morning. He was a little bit tired. Normally he will do the session tomorrow and then we will decide if he can be part of the under-21 game against Leicester next Monday.
“Florin is different – a different injury. He needs more time out, he needs more time to do training sessions.”