The 21-year-old Jagiellonii Bialystok stopper has attracted interest from across Europe after helping the club win the Polish Cup and producing some impressive appearances for the national side.
And a Jagiellonii Bialystok spokesman told Polish sports daily Przeglad Sportowy: "On Monday, we received a concrete offer from Swansea. For several weeks they have been very determined to buy Grzesiek."
Any move for Sandomierski is likely to raise further doubts over the future of Dorus de Vries at the Liberty Stadium.
The Dutchman has reportedly turned down a new contract offer from the Barclays Premier League new boys, with Wolves among the clubs said to be interested in recruiting the 30-year-old.
Source: PA
Source: PA