The Euro 2016 star is set to be the Tigers’ first signing since their return to the Premier League.
Robson-Kanu, 27, is on holiday mulling over a four-year contract offer from Hull, though Chinese Super League clubs, Watford, Swansea and Burnley remain interested in the free agent.
Hull manager Steve Bruce, however, is hopeful of tying up a deal with the player’s lawyer and father Rechi Kanu.
The former Reading striker scored the goal of Euro 2016 as Wales beat Belgium 3-1 in the quarter-finals and Bruce said: “I am hopeful but we face a bit of a competition. We have put a proposal to him, and he’s gone away to think about it.”
Bruce could also be bringing back another Welshman, James Chester, to the club 12 months after selling him to West Brom for £8m, though Bordeaux centre-back Lamine Sane is also a target.
Hull need defensive cover amid fears that Moses Odubajo dislocated his knee cap in the goalless draw at Grimsby on Friday night.
A scan tomorrow should show the extent of the injury.
Fellow Premier League newcomers Middlesbrough are also expected to make signings this week.
Coach Aitor Karanka hopes to tie up deals for Alvaro Negredo, Neven Subotic and Gaston Ramirez.
Valencia have agreed to send 30-year-old striker Negredo on loan, subject to the player passing a medical, and work permits must be secured before Subotic and Ramirez can sign.
Boro secured their sixth signing of the summer by landing Valencia right-back Antonio Barragan and speaking after Saturday’s 2-0 friendly win at Doncaster, Karanka said: “We need to build a squad for the Premier League. The better players we have, the more players we have, the greater chance we have of doing well next season.”
A deflected goal from Stewart Downing and another from teenager Alex Pattison handed Boro at the Keepmoat Stadium, with new boy Viktor Fischer making his debut.
Leeds United’s latest transfer target has walked out on his club.
Former Belgium Under-19 Anthony Limbombe left pre-season training at NEC Nijmegen without permission and will be disciplined if he does not return tomorrow.
Leeds have had a £1.8m rejected for Limbombe, who has a year left on his contract, by the Dutch club, who are wanting £3m.
Limbombe is known for his pace and eye for goal, scoring seven times and making seven more in the Eredivisie from wide-left last season.
Head coach Garry Monk is keen to add width to his Leeds squad, though he has Jordan Botaka, Stuart Dallas and Hadi Sacko as wingers.
Former Swansea manager Monk has already brought in six new players and is being linked with a former Chelsea defender.
Reports in Italy suggest he is keen on signing 33-year-old Valerio Di Cesare on loan from Serie B Bari to replace Giuseppe Bellusci, who has joined Empoli on loan.
Sheffield Wednesday reserve goalkeeper and former Wales international Lewis Price has signed a two-year deal with Rotherham United and is set to battle Lee Camp for the No 1 spot for the Millers.
The Owls are expected to sign Norwich City’s former Blackburn goalkeeper Jake Kean, 25, as cover tomorrow.
Second-half strikes from Harry Bunn and Jack Payne gave Huddersfield Town a 2-0 friendly win at Oldham, where former Boundary Park goalkeeper Joel Coleman, a £100,000 buy, played for the visitors as Slovenian centre-back Jon Gorenc Stankovic and Australian international midfield man Aaron Mooy made their first public appearances.
Oldham featured seven of their nine new signings, including on-loan Leeds United forward Lee Erwin.
Huddersfield striker Jordy Hiwula, 21, has joined Bradford City on a year’s loan.
New signing Tom Bradhsaw made his Barnsley debut and scored their final goal in a 6-0 win at Weston-Super-Mare, Stefan Payne scoring a hat-trick as all the goals came after the break.