The 25-year-old Norwegian is known to be keen on securing another English club after three years at Selhurst Park.
"If Jonathan wants to go there, there is a big chance it will happen," Roger Parr, Jonathan's father and advisor, told Aftenposten.
"At Ipswich, he will be first choice. Jonathan has had a meeting with the manager (Mick McCarthy) and they had a positive talk.
"We know that it is a really good club with a nice stadium and good supporters. That is important."
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