Celtic are set for a double swoop with Ukraine midfielder Anatoliy Timoshchuk and Holland striker Jan Vennegoor of Hesselink in the sights of manager Gordon Strachan.
Timoshchuk, 27, who plays for Shakhtar Donetsk, was part of the Ukrainian team which reached the quarter-finals in Germany, while PSV Eindhoven striker Vennegoor of Hesselink was a substitute in the second-round defeat by Portugal.
Celtic chief executive Peter Lawwell has already made an initial contact with Shakhtar Donetsk general director Sergei Palkin, who told the Daily Record: 'Peter Lawwell called me.
'It was an introductory call to express Celtic's interest in Timoshchuk, they have not yet made an offer.
'We are now waiting for them to send us an offer in writing.
'If we get an offer which meets a real valuation of our captain's worth, we will not stand in his way.
'I told Mr Lawwell about a previous offer from Feyenoord which was not acceptable and he now knows the price that would be acceptable to us.
'We are now waiting for Celtic to make an offer.'
Van Hesselink and his agent and father - also called Jan - are also set to meet Celtic.
Van Hesselink senior said: 'We have a meeting with Celtic tomorrow.
'Both parties know what is on the table and I think it looks good.
'Personal terms will not be a problem and it is up to the clubs to agree on a fee.'