West Ham's interest in Fulham's stars was knocked back in January but the Cottagers could be powerless to stop the East Londoners making Fredericks their first signing of the summer when the 25-year-old is available on a free transfer.
Cairney on the other hand will likely cost interested suitors a pretty penny after his fine displays for the promotion-chasing Cottagers this season.
He was at it again on Tuesday night, orchestrating Fulham's superb 3-0 win over Sheffield United.
"He won't be at Fulham next season, he's that good," McInally told Sky Sports.
"They can ask as much as they want.
"Not only was he composed, he was silky on the ball, he was so, so good."
The 27-year-old Fulham skipper has 21 goals from 102 games for the West London club and looks set to attract big interest again this summer, especially if Fulham fail to win promotion back to the Premier League.
Of course West Ham themselves are not certain what division they will be in next season.
But if they do survive and are serious about signing Moyes' fellow Scot then they will likely have to break the record transfer fee of £25million they paid for Marko Arnautovic last year.