Press Association Sport understands the former Aston Villa and Birmingham man will not be offered a new contract, with his existing deal due to expire at the end of next month.
The 27-year-old will join Carlos Cuellar and Andrea Dossena in leaving Wearside, with Poyet making decisions on a series of players who have reached a watershed with the Black Cats.
Gardner, who joined the club in a ?6million switch from Birmingham in June 2011, made 26 appearances last season, but only 12 of them were starts as he slipped in the pecking order.
Uruguayan Poyet indicated after Sunday's 3-1 home defeat by Swansea that the club would hold talks with "three or four" of a group of 11 men either out of contract or having reached the end of loan spells at the Stadium of Light.
Phil Bardsley, Jack Colback and Sebastian Larsson are the principle candidates, with Fabio Borini, who spent last season on loan from Liverpool a man Poyet would love to secure once again.
However, Colback's situation in particular is being monitored by a series of potential suitors with derby rivals Newcastle among them, and there is little doubt all four men will have options.
Their continued presence on Wearside was thrown into doubt by Sunderland's desperate fight against relegation, which looked to have been lost on several occasions.
The club has built pay-cut clauses into contracts since its last fall from the Barclays Premier League, but there is little doubt there would have been a significant restructuring of the squad had the worst come to the worst.
However, Poyet's outlook is now very different and while his aim is to prevent a repeat, he is keen to retain the services of those men who proved their worth when it mattered most and avoid the kind of wholesale change which saw 14 new players arrive at the club last summer under predecessor Paolo Di Canio.
Source : PA
Source: PA