The Tigers look to have won the race for Bertrand, who was also being courted by Tottenham and Southampton, while Amalfitano’s impressive loan spell with West Brom last season has convinced Bruce to return for him this summer, having missed out on him this time last year.
And a £9.75million double capture is close to being completed as Bruce hopes to build a squad capable of competing in both the Premier League and Europa League next term.
A source close to the KC Stadium said: “Even though Ashley Cole has been released by Chelsea, Ryan feels his opportunities at the Bridge will still be restricted because of the form of Cesar Azpilicueta.
“And he reckons his best chance of getting regular first-team football will be with Hull.
“Amalfitano really enjoyed his time at The Hawthorns and desperately wants to come back to England and play in the Premier League again next season.
“And one of the big attractions for Steve is that Morgan is a versatile performer who can operate equally well either in central midfield or out wide on the right.”
It is believed Bruce will pay £5.25m for Bertrand and £4.5m Amalfitano.