The 27-year-old has returned from his loan spell at fellow Scottish club St Mirren.
The Northern Irish commenced his career with Premier League club Watford for around four years.
He later had spells at Kilmarnock and Brentford before joining Ibrox in 2016.
Hudson proved to be a decent signing, as he made 18 appearances in his first season.
However, he fell down the pecking order, owing to his lack of form and was loaned to the Saints.
At St Mirren, Hudson was a regular in the playing 11 until his ankle injury hindered his progress.
Sparing his lay-off of 3 months, the versatile full-back made 20 appearances under Oran Kearney.
Now, with his contract set to expire at the end of this season, the Gers have no intentions of keeping him in Glasgow.
No place in the main team
Hudson’s traditional position is right-back, which is currently occupied by Tavernier, who is having a great season with Gers.
The English right-back was involved in 28 goals this season and has the tendency to play on the wings, which has made him a great asset for Steven Gerrard.
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The Gers have won their last three matches and are looking to extend their run with Aberdeen this Sunday.
In the previous meeting, the Dons defeated the Ibrox side in the Scottish Cup quarter-finals.