Police detectives have released a CCTV image of 53-year-old Jean Campbell who was found dead in Cranhill Park in Bellrock Street.
She was walking her German Shepherd dog Kai in the area when she was attacked.
The mum of three's body was discovered at around 7.40am on Saturday, December 14.
Detectives launched a murder hunt and are carrying out extensive enquiries in the area to trace the killer.
Crimestoppers is offering the reward to anyone providing information leading to the arrest and subsequent conviction of the culprit.
Detective Chief Inspector Colin Carey, of the Major Investigation Team, said: "A dedicated team of highly experienced detectives are working round the clock on this inquiry.
"Despite previous media appeals and a scene revisit on the evening of Friday, December 20, we have still to identify a motive for this brutal murder."
Mrs Campbell was last seen on CCTV at 10.30pm on Friday, December 13 as she was walking her dog along Bellrock Street in the direction of Cranhill Park.
She was wearing a black three-quarter length jacket and light coloured trousers.
Police have urged anyone who remembers seeing Jean that night, or recognises her description, to contact them.
They also wish to speak to anyone who has suspicions regarding friends, neighbours or family members who came home late on the evening of Friday, December 13 or early hours of Saturday, December 14 with unexplained injuries or dirt-stained clothing.
The killer could have sustained minor injuries to their face or body and may be acting out of character.
There is a possibility their clothing may be dirty or stained with muck or grass.
Detective Chief Inspector Colin Carey said: "The local community has been keen to assist police; however, I am sure there are people who have information that could assist our investigation who, for whatever reason, have yet to contact police.
"If you have any information whatsoever that may assist the inquiry, no matter how insignificant you think it is, please come forward and share that information with us.
"I would also like to reassure local people that there are extra police patrols in the area, and anyone with any concerns should speak to officers."
A spokesman from Crimestoppers urged anyone with information to contact their hotline where information can be given anonymously.
He said: "This is a tragic ordeal for the family of Jean to have to go through and they deserve answers as to why this has happened and who is responsible.
"The person or people who committed this murder should not be allowed to get away with their actions, and for this reason we would urge anyone with information to come forward and contact Crimestoppers anonymously, safe in the knowledge nobody will ever know you spoke to us."
Anyone with information should contact police at the incident room at Baird Street Police Office on 0141 532 4191, the Police Scotland non emergency number 101, or the dedicated email address firstname.lastname@example.org.
Alternatively, contact Crimestoppers on 0800 555 111 or at www.crimestoppers-uk.org