The young Mexican, who finished third in this year's GP2 series, has been heavily linked to a promotion to the Swiss team's full race line-up in place of his McLaren-bound countryman Sergio Perez for next season, with Nico Hulkenberg appearing likely to get the other seat in place of Kamui Kobayashi.
Gutierrez has become a regular for Sauber over recent years in the young driver test sessions and has been given the nod to complete two days in the C31 in the days following the Yas Marina circuit's grand prix in two weeks' time.
The 21-year-old will complete the final two days of the test, Wednesday and Thursday, with the team to use the opening day to assess rising Dutch talent Frijns, who is the same age as Gutierrez.
Frijns is in the running to be crowned this season's Formula Renault 3.5 champion ahead of the category's season finale at Barcelona this weekend and the young driver test will mark his debut at F1 level.
Should there be no announcements confirming Sauber's full 2013 race line-up before the November 6-8 test, Gutierrez's appearance at Yas Marina is likely to be billed as his final audition for a race seat.