Bullard spent the second half of last season on loan at Ipswich from the Tigers and Jewell has said that he is keen to see the midfielder return to Suffolk.
However, the Championship club face competition for his signature from some Premier League sides.
"[Bullard] says he's got a couple of Premier League teams that are showing interest," Jewell told a press conference.
"But I told him I am very keen and he said he will consider us.
"If he goes to a Premier League team we won't be able to compete. But we'd like to bring him here."
Bullard scored five times during his six-month spell with Ipswich.