Fay (77) was reported missing at about 1.50pm on Friday and was last seen in the Barwick Road area.
She is described as white, 5ft tall with very blonde shoulder-length hair.
The 77-year-old was last seen wearing a red T shirt, denim jacket, black/red flowered ankle dress and was carrying a straw bag.
Officers are conducting a number of searches to find Fay and are very concerned for her welfare.
Anyone who sees her is asked to ring Leeds CID on 101 referencing police log 879 of July 7.