Both Scots joined Las Palmas this season, with McKenna arriving from Nottingham Forest and McBurnie from Sheffield United.
"It was a great opportunity for us. A different league and a top league. Unless you play for a Champions League team, you probably never get the chance to meet Madrid or Barcelona," McKenna told the Guardian.
McBurnie chimed in: "I tried to convince them not to pick up Scott!
"When I arrived, the sports director asked me about Scott. We have been playing together for several years and he was contract free just like me.
"Many of the clubs that made offers to us were the same. They were obviously interested in a particular style – something British."
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