The Swedish international joined the newly-promoted Blues on a season-long loan from Italian club Napoli last summer after Brentford had pulled out of a deal at the medical stage.
It took a while for the 25-year-old, who is managing a knee issue, to build up his robustness levels. The classy midfielder ended the relegation season as one of the team’s top performers though.
Had Town stayed up then they would have been obligated to sign Cajuste for around £10m. He still has three years left on his contract, Napoli having reclaimed the Serie A title in his absence.
“Jens is a loan player who I think has done really well for us,” said Ashton.
“He's had some challenges with injury this season, which have been well documented.
“Our conversations with Jens are ongoing. A deal or Jens to be here for the long term, it would need to be something that's right for us, him and his club - and that dialogue continues.”
Cajuste was the only one of Town’s four loan players to feature in the season ending 3-1 home defeat to West Ham.
Asked if that meant there was a chance the midfielder could stay, Blues boss Kieran McKenna replied: "We've loved having Jens here, but there's probably a lot to do for that to happen. We'll see what the next few weeks brings.”
Cajuste has now played top flight football in Denmark, France, Italy and England.
Speaking exclusively to the EADT and Ipswich Star back in March, he said: "We'll see where it goes. I've enjoyed my time so far here, definitely, so that's all I can say right now.
“I think Suffolk does suit me. I'm pretty relaxed, pretty laid back, so I think it suits me like a hand in the glove. I think it's perfect for me.”
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