The 27-year-old’s contract is due to expire at the end of next season but Killie wants to cash in on him this summer.
The Scottish full-back spent his youth years with the Hoops as well as Aberdeen.
He has made 37 appearances this season and was acclaimed for his defensive stats.
O’Donnell commenced his professional career with Patrick Thistle and went to make more than 100 appearances.
He also had notable spells with Luton Town before he moved to Rugby Park in 2017.
O’Donnell has been an integral part for Steve Clarke’s side, making 87 appearances in two seasons. The full-back has also earned 7 caps for his national side.
Why the Celts should move for O’Donnell?
The Hoops seem to have less options for the right-back position and they rely heavily on Mikael Lustig.
The Swedish full-back is also wanted by his country’s club Malmo, which leaves the Hoops in big trouble now.
Jeremy Toljan, who was bought on loan from Borussia Dortmund to ease the pressure of Lustig, failed to make his mark. Now, the German youngster is set to make his return to Bundesliga this summer.
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O’Donnell would be a smart addition for the Hoops given his experience in Scottish League. Furthermore, he is highly known for his defensive capabilities and can form a high line of defence with fellow stars Simunovic, Kristoffer Ajer and Kieran Tierney.
The Hoops beat Hearts 2-1 in the Scottish Cup final.