Saints make Andrei offer
The Saints boss will run the rule over the Rangers winger, who was released by the Ibrox outfit at the end of last season.
Although Strachan has not guaranteed the Ukrainian a contract, there is an offer to train with the South Coast club for 7-10 days, starting next Monday.
Following the trial, there will be discussions between Strachan and Kanchelskis in a bid to determine whether he will sign a deal with the Premiership club.
Kanchelskis was a firm favourite during his days at Manchester United, but was sold to Everton before eventually ending up in Scotland with Rangers.
Gillingham boss Andy Hessenthaler recently revealed he rejected the opportunity to sign the 33-year-old midfielder, whose last spell in England was during a loan stint with Manchester City.