The pair travelled with the Boro squad to Doncaster for Saturday’s pre-season friendly as they finalise moves to the Teesside club.
Following the 0-0 draw with Rovers, Karanka said: “I hope (Fabbrini and Stuani will sign) because the club is working (on it), they are with us but we need to finish the paperwork.
“Hopefully they can be with us as soon as possible and both of them are going to be very important players for us.
“They are both players who wanted to join us and they had better contract options available, but they wanted to join us. If we can finally sign them then they are going to improve the squad and I’ll be very pleased if they can sign.”
Uruguayan striker Stuani will join from Espanyol, while midfielder Fabbrini, who spent spells on loan at Millwall and Birmingham last season, will make the switch from Watford.