Tigers boss Steve Bruce is back from holiday and is ready to step up his efforts to bring in new players ahead of next season's Premier League campaign, with the duo high on his priority list.
Bruce is keen to get Schmeichel on board and has already failed with one bid of £1.25million for the goalkeeper, who Leicester value in the region of £4million.
However, with just over a year remaining on his current contract, Bruce is unwilling to go anywhere near that figure and it is thought his next offer will be just short of £2million.
Meanwhile, Bruce is also said to be keeping tabs on Clarets midfielder McCann, who will be available on a free transfer when his contract expires at Turf Moor.
A host of Championship clubs are also keen but the chance to play in the Premier League should sway the player towards the Tigers.