Swansea boss Garry Monk is adamant that only an “astronomical” bid could prise Wilfried Bony away from the club.
Everton manager Roberto Martinez hopes to complete the signing of midfielder Muhamed Besic in the near future.
Aluko is currently sidelined by a long-term Achilles injury that cut short an impressive start to the season from the former Rangers man, but he remains key to manager Steve Bruce's plans.
His previous deal was due to expire at the end of the season and talks have been ongoing for a matter of months.
The 24-year-old rejected terms in November and discussions were put on hold after injury struck, but with both sides keen to continue their relationship, he has put pen to paper on an improved contract.
"I'm happy to stay here,"he told the club's official website.
"I've said right from the beginning, when talk about a new deal first came about, that I was happy here."Aluko brushed aside speculation that a move had been on the cards during his contract deliberations, adding: "I said it might take time for the deal to happen and that is how it turned out. Because it took a while people started making a story out of it and were saying I was going to this place or that. That was always irrelevant.
"I'm glad that it's done, but I never really thought that it wouldn't happen. I'm happy here and things have turned out the way I thought they would.
"When I first signed, I said that the team was good enough to get into the Premier League and I felt that my second year here would be in the top flight.
"That is how it has worked out and I'm happy about that."
Hull vice-chairman Ehab Allam said: "We are delighted that Sone has signed a new deal with us. When we sat down with Steve to identify potential targets for January, he was also keen to discuss the possibility of extending Sone's contract as it was due to expire in the summer. As part of our ongoing commitment to improve the playing squad, we decided that it was in our interest to act now and agree a new deal for such an exciting player."
Aluko is back training outdoors and is expected to be in contention for first-team action in around a month.
Having also missed a large period of the last campaign due to injury, he will be desperate to prove himself once again.