The 82-year-old was threatened by two masked men who came to the door of his home in Gillies Lane, Baillieston, at 22:15 on Thursday.
The attackers pushed the pensioner and demanded money, before searching the house and leaving empty-handed.
Both men were wearing balaclavas and dressed all in black. Police have appealed for information.
The men, one of whom is thought to have been wearing a black "puffa" or bomber jacket, made off in the direction of Bredisholm Road.
Det Sgt Raymond Hunter, from the community investigations unit in Pollok, said the incident was "very frightening" for the victim.
He said: "We have been checking CCTV and speaking to neighbours but need to hear from people who may have been in the area at the time. There is a pub at the top of the lane on Bredisholm Road, so we would appeal to patrons from there to get in touch if they saw or heard anything.
"At this time we still have to establish why the man was targeted. The suspects seemed to think he had a significant amount of cash in his home, which was not the case, hence the reason they left empty-handed.
"Whether this was mistaken identity or a rumour, we do not know, but in any case to subject an elderly man in his home to this, is not just wrong, it was cowardly."

Celtic skipper Scott Brown has led Gordon Strachan's national team recently but fit-again Fletcher is back playing at West Bromwich Albion.
"Scott has flourished under it when Darren's been injured," Wilson told BBC Radio Scotland.
"But Darren's more the leader of the country and has been for many years."
Wilson, who won his only international cap against Northern Ireland in 2011, added: "We're lucky that we've got two inspirational players in the middle of the park that can take that role.
"It is probably the biggest honour you can receive in football, so I think it matters a great deal, especially to the players involved - Scott and Darren.
"It will be of great importance to both of them, but I don't think either of them will be too disappointed or let it affect their game if they are not selected as captain."
Wednesday's friendly against Michael O'Neill's side at Hampden comes before Scotland's next Euro 2016 qualifier versus Gibraltar on Sunday.
"This game has been well selected by both sides," said Wilson, who now plays for Dumbarton after spells at Dundee United and Celtic.
"Quite often you can have these international friendlies that sort of peter out into nothing - a kind of drab affair.
"But with two competitive teams and players that have played against each other at the highest level in England and Scotland coming against each other, it gives it that extra bit of needle that you need."
An elderly man has been assaulted in his Glasgow home during an attempted robbery.
[NEXT_CONCEPT]
Darren Fletcher's past experience leading Scotland could win him the captaincy against Northern Ireland, says former international Mark Wilson.