The 25-year-old Puncheon spent loan spells with Millwall and Blackpool last season after finding himself pushed to the fringes at St Mary's by 17-year-old starlet Alex Chamberlain.
Puncheon returned to Saints this summer but did not go on the club's pre-season tour to Switzerland and has not been given a squad number.
With his future at Southampton looking bleak, it appears the former Barnet and MK Dons winger could be set for a move to west London.
Press Association Sport understands Neil Warnock has approached the south coast club with a bid for Puncheon that includes centre-back Gorkss heading to Saints.
The Latvia international joined the Loftus Road outfit from Blackpool in 2008 and last season helped them to the npower Championship crown.
While Gorkss' move may come as a surprise, Puncheon's departure has been on the cards all summer.
QPR, Blackpool, Millwall, West Ham and Birmingham have all been mooted as potential suitors and Puncheon's agent Tony Finnigan admitted earlier this month that his future lies away from St Mary's.
"Southampton don't want him there. They want to sell him, so people are being encouraged to enquire," he said.
"He is a good player but (Southampton manager) Nigel Adkins doesn't want him. He has gone from playing at Old Trafford to playing with the Under-16s."
Source: PA
Source: PA