The 30-year-old Dutch international is understood to have undergone tests at the club's training base on Tuesday.
The Cottagers are now close to formally announcing the arrival of the shotstopper, according to Goal.com.
Stekelenburg, who has won 54 caps for the Netherlands, joined Roma from Ajax in 2011.
Restore Data
| Team | P | W | D | L | F | A | GD | PTS | |
| 1 | Napoli | 13 | 9 | 2 | 2 | 20 | 9 | 11 | 29 |
| 2 | Atalanta BCAtalanta | 13 | 9 | 1 | 3 | 34 | 16 | 18 | 28 |
| 3 | Inter Milan | 13 | 8 | 4 | 1 | 31 | 14 | 17 | 28 |
| 4 | Fiorentina | 13 | 8 | 4 | 1 | 27 | 10 | 17 | 28 |
| 5 | Lazio | 13 | 9 | 1 | 3 | 28 | 14 | 14 | 28 |
| 6 | Juventus | 13 | 6 | 7 | 0 | 21 | 7 | 14 | 25 |
| 7 | AC Milan | 12 | 5 | 4 | 3 | 20 | 14 | 6 | 19 |
| 8 | Bologna | 12 | 4 | 6 | 2 | 15 | 16 | -1 | 18 |
| 9 | Udinese | 13 | 5 | 2 | 6 | 16 | 19 | -3 | 17 |
| 10 | Empoli | 13 | 3 | 7 | 3 | 10 | 11 | -1 | 16 |
| 11 | Torino | 13 | 4 | 3 | 6 | 16 | 19 | -3 | 15 |
| 12 | Roma | 13 | 3 | 4 | 6 | 14 | 18 | -4 | 13 |
| 13 | Parma | 13 | 2 | 6 | 5 | 17 | 21 | -4 | 12 |
| 14 | Hellas VeronaHellas Verona | 13 | 4 | 0 | 9 | 17 | 32 | -15 | 12 |
| 15 | CagliariCagliari | 13 | 2 | 5 | 6 | 14 | 24 | -10 | 11 |
| 16 | Genoa | 13 | 2 | 5 | 6 | 11 | 24 | -13 | 11 |
| 17 | Como | 13 | 2 | 4 | 7 | 13 | 25 | -12 | 10 |
| 18 | Monza | 13 | 1 | 6 | 6 | 11 | 16 | -5 | 9 |
| 19 | Lecce | 12 | 2 | 3 | 7 | 5 | 21 | -16 | 9 |
| 20 | VeneziaVenezia | 12 | 2 | 2 | 8 | 11 | 21 | -10 | 8 |
| > Serie A Full Table | |||||||||
