The Saints’ top scorer from the last four seasons recently completed a £4m switch to hometown club Liverpool, leaving a gaping hole up top.
One of Koeman’s main tasks for the remainder of the transfer window is to get in a replacement for him, with Wickham an option.
The 21-year-old came to the fore for the Black Cats towards the back end of last season, netting five key goals as the North East side pushed clear of relegation.
Wickham had spent the part of last term on loan in the Championship with Leeds, and has largely failed to justify the reputation he earned in his teenage years.
The youngster has just a year left on his contract, and Southampton hope that they can get him on the cheap.
Sunderland may be keen to cash in, with Gus Poyet looking to snap up Fabio Borini from Liverpool after being impressed by his form at the Stadium of Light last season during a loan stint.