Hoops boss Hughes will try to do a £3.5million deal for the 21-year-old, who has found the net on a regular basis for club and country since leaving his homeland in 2008.
Bern will sell if the price is right, leaving the west Londoners to obtain work permit for Mayuka, who moved to Switzerland in 2010 following a two-year spell at Israeli side Maccabi Tel Aviv.
That should not be a problem as the 5ft 9in frontman has played 36 times for Zambia in serious competition, scoring 10 goals.
Meanwhile, QPR centre-back Matt Connolly is close to a move back to the Championship with Cardiff.
The Londoners have accepted a bid from the Welshmen for the 24-year-old, who has won back-to-back Championship titles with Neil Warnock’s Hoops in 2011 and then while on loan at Reading last season.