Arsenal are hopeful of reaching an agreement with the Scottish champions over a deal for the full-back, despite seeing two offers worth £15m and £25m already rejected this summer.
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It is believed Parkhead chiefs are demanding £30m for the 22-year-old, and Van Dijk has stated he was aware of the defender’s talent during their time together in Glasgow.
Asked about Tierney possibly moving from Scotland to England, Van Dijk told the Daily Record: “It is not an easy step to make and you have to play well to do it, but he has the qualities.
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“Kieran made his debut against Dundee when I was at Celtic. I scored a free-kick up there and then he came on and helped us get the win.
“You could tell he was a good player who would do well.”