The 30-year-old departed the Scottish club this summer after failing to agree terms with Charles Green's new company, and is therefore without an employer.
Besiktas's official website confirmed the talks, and he could reportedly complete a deal before the end of the week.
McGregor has 21 Scottish caps to his name.
Restore Data
| Team | P | W | D | L | F | A | GD | PTS | |
| 1 | GalatasarayGalatasaray | 19 | 16 | 3 | 0 | 52 | 22 | 30 | 51 |
| 2 | Fenerbahce | 18 | 13 | 3 | 2 | 45 | 18 | 27 | 42 |
| 3 | Samsunspor | 19 | 11 | 4 | 4 | 32 | 18 | 14 | 37 |
| 4 | Goztepe SKGoztepe SK | 18 | 9 | 4 | 5 | 37 | 23 | 14 | 31 |
| 5 | BesiktasBesiktas | 19 | 8 | 7 | 4 | 28 | 20 | 8 | 31 |
| 6 | EyupsporEyupspor | 18 | 8 | 6 | 4 | 29 | 19 | 10 | 30 |
| 7 | Istanbul BasaksehirIstanbul | 19 | 8 | 5 | 6 | 31 | 25 | 6 | 29 |
| 8 | GaziantepGaziantep | 19 | 7 | 5 | 7 | 25 | 26 | -1 | 26 |
| 9 | Caykur RizesporCaykur Rizespor | 19 | 7 | 3 | 9 | 19 | 29 | -10 | 24 |
| 10 | TrabzonsporTrabzonspor | 18 | 5 | 7 | 6 | 30 | 24 | 6 | 22 |
| 11 | AlanyasporAlanyaspor | 18 | 5 | 7 | 6 | 19 | 21 | -2 | 22 |
| 12 | KasimpasaKasimpasa | 18 | 4 | 9 | 5 | 24 | 30 | -6 | 21 |
| 13 | AntalyasporAntalyaspor | 18 | 6 | 3 | 9 | 21 | 37 | -16 | 21 |
| 14 | KonyasporKonyaspor | 18 | 5 | 5 | 8 | 21 | 28 | -7 | 20 |
| 15 | SivassporSivasspor | 18 | 5 | 5 | 8 | 21 | 28 | -7 | 20 |
| 16 | Bodrumspor | 19 | 4 | 4 | 11 | 14 | 25 | -11 | 16 |
| 17 | KayserisporKayserispor | 18 | 3 | 7 | 8 | 17 | 34 | -17 | 16 |
| 18 | Hatayspor | 19 | 1 | 7 | 11 | 17 | 32 | -15 | 10 |
| 19 | Adana Demirspor | 18 | 2 | 2 | 14 | 15 | 38 | -23 | 5 |
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