Celtic have reportedly rejected another bid for Matt O'Riley - this time from Southampton.
There is strong transfer interest in the Denmark international this summer.
And with the Scottish Premiership season less than a week away now, more offers could be on the horizon for the 23-year-old.
The Sun claims that Celtic have knocked back Saints' initial offer.
Head coach of the newly-promoted English Premier League side Russell Martin is a big admirer of the attacking midfielder.
He signed the English-born player for MK Dons before he eventually joined Celtic in January 2022 for £1.5m.
It remains to be seen whether Saints will come back in for the Premiership star.
Italian outfit Atalanta have already had three bids rejected by Brendan Rodgers & Co.
The Europa League champions' most recent offer reportedly landed at the end of last week but fell short of Celtic's valuation of the player.
Another report in the Daily Mail states that the Serie A team will likely 'increase their offer' before the big league kick-off against Kilmarnock on Sunday afternoon.
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Celtic transfer news & rumours as window opens
Meanwhile, Reo Hatate is a transfer target for Leicester City, according to a report.
The Foxes are back in the big time after their Championship title triumph last season under Enzo Maresca, who has now moved on to Chelsea.
Steve Cooper is the new head coach, and he will guide them into the new English Premier League campaign on Monday, August 19 with a home match against Ange Postecoglou's Tottenham.
They could go into that match with Scottish Premiership ace Hatate in their ranks, according to the Daily Mail.
They state that Leicester are readying a 'big money offer' for the Japanese international.
Hatate, 26, joined the Hoops from Kawasaki Frontale in January 2022 and made an instant impact on the team by scoring against Hearts and Rangers. He has 16 goals in 87 matches to his name.
