The Bhoys did complete two deals on the final day of the transfer window, snapping up DInamo Zagreb defender Jozo Simunovic and Inverness midfielder Ryan Christie, making it eight signings for Celtic this summer.
Manager Ronny Deila had previously signed Logan Bailly, Saidy Janko, Dedryck Boyata, Tyler Blackett, Scott Allan and Nadir Ciftci - and despite the latter being a forward, more strikers have been linked, especially since Stefan Scepovic signed for Getafe on Monday.
The Daily Mail report that Celtic did indeed push to sign a forward - but failed in moves to sign Swansea's Michu and Sunderland's Steven Fletcher.
Fletcher, 28, was always going to be a long shot despite being a Scottish international, but Michu has no future at Swansea, even after his stunning 2012-13 season.
The 29-year-old Spaniard hit 22 goals in his debut season with Swansea, but has since failed to replicate that form, and spent last season on loan at Napoli.
With no role to play under Garry Monk at the Liberty Stadium, Swansea had been hoping to find a suitor for the forward - but the Daily Mail believe that a move to Celtic failed late on deadline day.
That means Deila must now make do without a new forward, putting the onus on Leigh Griffiths and the aforementioned Ciftci to lead the line and score goals on a regular basis.