The former Watford midfielder has made 14 appearances for Town since joining the club on loan, scoring twice.
His deal expired last week though allowing Hand to feature for Hayes during their 3-1 defeat against promotion hopefuls Fleetwood Town on Tuesday night.
Hand, who started his career at Watford, signed a season-long deal for Hayes in the summer, so Luton would need to pay a fee for his services, but the emergence of youngster Godfrey Poku, currently on loan at Southport, may give Town manager Gary Brabin food for thought when the transfer window opens.
Hayes boss Bashir said: “We are not sure what is happening at the moment.
“Luton have got first refusal on him, but whether they sign him or not, that decision has not been made yet.
“We have got to see what they do and then on the back of what they do, we will make our decision from there.”
Luton assistant boss Alan Neilson added: “We spoke to them (Hayes) after his loan ran out with us, so he might as well go there and play a few games and try and do us a favour.
“He’s their player, so we just have to look at the situation again in January. The games Jamie’s played, he’s done well and he’s an absolutely great pro and great to have around the place.”
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