The Bhoys are in the market for a new striker having seen John Guidetti's loan deal from Manchester City expire, and assistant manager John Collins admitted to Sky Sports on Tuesday that an offer has been made for Turkish forward Ciftci.
The 23-year-old hit 16 goals for Dundee United last season, maintaining his reputation as one of the deadliest strikers in the Scottish Premiership.
However, with just one year left on his contract at Tannadice, Dundee United are vulnerable to losing their star striker this summer - and Celtic are ready to pounce.
The Scottish Sun report that, after having a £900,000 bid rejected for the forward, Celtic are now considering another bid to land Ciftci this summer.
However, it could all be too late, with the report also stating that English League One side Wigan Athletic - managed by former Celtic defender Gary Caldwell - have agreed a £1m deal with Dundee United to take Ciftci to the DW Stadium.
Celtic or Wigan?
If Wigan have had that £1m bid accepted, Celtic may need to better that offer given that Dundee United sold them Gary Mackay-Steven and Stuart Armstrong in January, and are seemingly unwilling to sell another key player to Celtic, according to the Scottish Sun.
Ultimately, if it comes down to Ciftci having to choose between signing for Wigan or forcing through a move to Celtic, then he should choose the latter.
Wigan are playing in the third tier of English football whilst Celtic will be favourites for the Scottish Premiership title - and can offer Champions League football too, making this decision a no-brainer for Ciftci.