Inspector Richard Hammond from Grantham Police Station, who is co-ordinating the continuing search for Mr Foster, says they have now spoken to someone who knows Mr Foster well.
He said: “That person was on the Long Bennington bus and saw Jack waiting at Stand 5 – from where buses go to Bottesford – and thought it strange that he was not getting on the Long Bennington bus.
“It is not known if Jack caught the Bottesford bus or was just using stand 5 waiting for another bus. He could have even returned to Grantham Town centre, the trail stops at this point in time.
It was about 2.35pm on Tuesday when Jack was wearing the clothes in the latest photograph police released yesterday – a brown ¾ length anorak type coat with a hood, what appears to be a green deer stalker hat, dark trousers and brown shoes.
Insp Hammond said: “If Jack has not had shelter for the last four nights since he was last seen – particularly last night when it snowed heavily – we are concerned he possibly could not have survived that weather.
“We have previously asked people living in the north part of Grantham to check their outbuildings and sheds for any trace of someone sheltering there. In view of the new information from the bus station, we are now widening our search into Leicestershire and asking our colleagues there, particularly in the Bottesford area to conduct similar searches and enquiries to the ones we have been making,” he said.
“A key to getting this information to the majority of people is getting media coverage and I hope we can generate some interest in Leicestershire as well now.”
Mr Foster went to Grantham Hospital on Tuesday for treatment to a fractured shoulder.
Because of that and his age he has very limited mobility and tends to shuffle rather than walk – so he has a distinctive gait and that coupled with the deer stalker hat, long brown anorak type coat anyone seeing him should remember him.
Police say they need to hear from anyone with any information and ask them to call 101 and quote Lincolnshire Police Incident number 392 of 23rd December.