The club are also in discussions with centre-back Reece Burke and George Long about staying.
Magennis was part of the side relegated from the Championship in 2020, Jones a new signing last summer, but both were very important parts of the Tigers' title win.
Northern Ireland centre-forward Magennis scored 20 goals in all competitions last season, seven in the final eight matches as the club closed out promotion. Perhaps as importantly, he was a very vocal leader on and off the field.
Jones, who joined as a free transfer from Southampton in September, fluctuated between centre-back and central midfield and impressed in both roles, starting 27 League One games including an unbroken run of the last 15 matches.
Centre-back Burke and goalkeeper Long both played in July's 8-0 defeat at Wigan Athletic last season.
Burke recovered to make 31 league starts last season. Long lost his status as first-choice goalkeeper this season, swapping with Matt Ingram in that respect, but the Tigers are still interested in keeping him after seven clean sheets in 13 games.
Left-back Max Clark has been released without making a first-team appearance but the rest of the squad remains under contract.
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