The 30-year-old, who started his career with Marseille, moved to Wales in June 2015, before heading to West Ham for a fee of £20.5m in August 2016.
He then returned to Swansea for £18.5m in January 2018, before a season-long loan move to Turkish side Fenerbahce last term.
However, Ayew is now back in the fold at the Liberty Stadium, scoring nine goals already, as Jones said: "He’s only 20 million and we’ve got to deal with him.
"He's a powerful player, he hits the target, he scores goals, but it's about us.
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"We want to impose ourselves on the game both off and on the ball and that's what I expect us to do."
Jones is taking on a club that he was once assistant manager, as he was appointed number two to Roberto Martinez back in 2007.
On his time in Wales, he said: "Just really fond memories. It was the start of our coaching career, we took on a wonderful football club who had been in the doldrums for a while and gave them a pattern of play in League One, that I think stood them in good stead for 10 years.
"They’ve reverted back to that, the last two appointments with Graham (Potter) and Steve Cooper, so I think it's a style that's worked with them through the years, and that's what we can expect to see."
The Swans appointed England U17 boss Cooper in the summer, the new boss leading his country to U17 World Cup success two years ago, as Jones added: "I’ve heard of him and you can see his method of work in their play.
"I don’t know Steve personally, I’ll hopefully have a drink with him after the game tomorrow but I love how his teams play that's for sure and it will be a difficult game."