Jahic is available on a free transfer after leaving Turkish side Karabukspor and he will spend the next few days training with Tommy Wright's squad.
The 31-year-old is primarily a centre-half, and his former clubs include AEK Athens and APOEL Nicosia, the latter of whom he represented in the UEFA Champions League.
Woods, meanwhile, has been without a club since leaving Doncaster in the summer, and he has since trained with Bristol City and Chesterfield.
"Both boys have been recommended to me and we will have a look at them and take it from there," said Saints boss Wright on the club's official website.
He added: "If we like the look of Sanel we could offer him a short-term deal and we'll monitor Martin, who plays left midfield, an area we are keen to strengthen."