The Blues boss is desperate to boost his attacking options ahead of the new Premier League season and has been linked with a number of players around Europe.
With the deal for Porto frontman Hulk reportedly on the brink of breaking down Di Matteo has been forced to cast his gaze further afield and set his sights on Schurrle.
The 21-year-old has firmly established himself as one of the brightest striking talents on the continent following a series of impressive displays for Germany at Euro 2012.
His progress since joining Leverkusen from Mainz last year can only described as rapid leading to rumours suggesting the West London club had tabled a formal bid with the Bundesliga club.
Chief executive Wolfgang Holzhauser admitted that the Champions League winners had made an appealing offer that was rejected after Schurrle stated he wanted to remain at the BayArena.
Hay was quoted as saying by German news agency SID: “We were presented with a very concrete offer from Chelsea for Andre of beyond the 20 million euro mark. The sum was pushed back and forth between the two clubs. We ultimately chose Andre.
“Andre is very valuable for us. He has also made it clear he would like to stay with us.”
Napoli forward Edinson Cavani has also been linked with a move to Stamford Bridge this summer along with Atletico Madrid’s Falcao but it seems Di Matteo and Chelsea owner Roman Abramovich have lost interest in the duo.
Borussia Dortmund frontman Robert Lewandoswki is said to be the new name on their transfer hit list and will rival Tottenham Hotspur for the £20 million rated Poland international.