The Welshman has admitted he is not sure of the midfielder’s future, with the Iceland star linked to a number of clubs including Brendan Rodgers’ Liverpool this summer
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Jenkins’ side agreed a club-record transfer fee of £6.8 million for the forward last month but the completion of that deal was thrown into doubt when manager Brendan Rodgers departed for Liverpool.
"There is always that risk when you take a player on loan that he does well for you and other clubs then become interested," Jenkins told the South Wales Evening Post.
"The fact is that he is Hoffenheim's player, not ours, and at this stage I have no idea whether he will be coming back to us on a permanent basis.
"Gylfi's agent hasn't told me anything about what's happening."
Reports have suggested that Sigurdsson could follow Rodgers to Anfield and Jenkins was frustrated to see the deal grind to a halt.
"For whatever reason they have decided to draw out the process and we will probably find out a lot more about what Gylfi's decisions are over the next few weeks," Jenkins explained.
"I have got no idea what the timescale is to sort things out as far as Gylfi is concerned.
"As things stand, I can only assume that he will be back at Hoffenheim come the start of pre-season training."