The 23-year-old featured for Poland in their recent encounter with England, but was unable to help his side avoid a 2-0 defeat at Wembley.
Klich has been impressive with Dutch side PEC Zwolle of late, alerting a number of clubs from across Europe.
Stoke and Fulham are thought to be at the front of the queue for the talented 23-year-old, and could make winter moves.
His current employers are believed to value him at around £1m, but are hopeful that the two clubs could start a bidding war, which may substantially increase the figure.
Klich joined PEC from Wolfsburg on loan in January before making a permanent move to the Eredivisie in the summer.
He has started the new campaign brightly, notching one goal and four assists so far.
Fulham boss Martin Jol is believed to be keen to bolster his options in the New Year in a bid to keep his side clear of the relegation zone, while Mark Hughes also sees Klich as the ideal man to help continue his Stoke revolution.
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