The defender is not in the plans of manager Mikel Arteta, who may even want to sign a new left-back in the summer.
Tierney has been impressive during a loan spell at Real Sociedad, but not enough to warrant an Arsenal first team recall.
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He told the Athletic: You get one career and you don't know how short or long it is going to be, so you have to try everything and make the most of it. I could see myself playing in Spain or Italy.
I love La Liga. It's a great league and I've enjoyed this season a lot.
I don't want to be jumping about to loads of different places, though. I want to get used to it and adapt to it, so I can kick on."