Their initial bid of £500,000 was below Wolves’ asking price of £1.5m, but the English side are keen to reduce their wage bill after being knocked back to League One.
Celtic believe that at 29, Doyle may not have a huge re-sell value at this stage in his career, so are hoping their £75k offer will be accepted.
Boss Neil Lennon is keen to add more firepower to his squad after losing Gary Hooper and Victor Wanyama over the summer.