The released Sunderland man had been hoping to reunite with Brendan Rodgers at Parkhead.
With Brendan Rodgers beginning to get his Celtic transfer plans underway following his appointment, the Glasgow Evening Times has reported that one deal which won't be happening is that of released Sunderland striker Danny Graham.
The 30-year-old forward has not had his contract renewed at the Stadium of Light and speculation had surfaced in recent weeks linking him with a reunion with his former Swansea City manager Rodgers at Parkhead.
Celtic appears to be in the market for a new frontman to provide competition for 40-goal top scorer Leigh Griffiths next season, and Graham's name had been one of those mentioned as a leading candidate.
The former Carlisle United and Watford man thrived under Rodgers in south Wales, scoring 12 goals in 36 league appearances in the Swans' first Premier League season.
However, despite the prospect of renewing that partnership, the Evening Times claims that the Bhoys and Rodgers have ultimately decided not to move to bring the striker to Glasgow, and that Graham will instead undergo a medical at Blackburn with a view to signing a permanent deal.
Celtic's reservations would be understandable; Graham will turn 31 in August and has been far from prolific in recent years, although he did net seven in 18 appearances during his loan spell at Ewood Park in the latter half of the season.
Instead, it is thought that the Bhoys will turn their attentions to Bristol Rovers star man Matty Taylor as they look to add more firepower, with the 26-year-old having smashed 27 goals last term in the fourth tier of English football.