Maguire, 24, is expected to leave the KCOM Stadium in the summer after Hull's relegation to the Championship, with Spurs reported to be leading the queue for his signature.
However, the Sunday Mirror says Everton boss Ronald Koeman is also interested in Maguire as he is unsure whether he can sign Burnley defender Michael Keane, who has been linked with Liverpool and Manchester United.
Maguire has a year left on his contract with Hull, with the Tigers expected to demand around £22m for his signature.
The 24-year-old said earlier this month that he would hold talks with Hull about his future at the end of the season.
"There were talks a couple of months ago and we came to an agreement, obviously with the position that the club is in, that we needed to totally focus on my football. I thought it wasn't the right time to speak," Maguire was quoted as saying by the Yorkshire Post.
"I still have a year left on my contract and am contracted to Hull City. But I am sure we will speak in the summer over another contract."
The Mirror says Spurs scouts have been keeping tabs on Maguire and have been sufficiently impressed with his performances to recommend him to club chairman Daniel Levy and manager Mauricio Pochettino.
The report added that the centre-back was keen on experiencing Champions League football with Tottenham.
However, with Toby Alderweireld and Jan Vertonghen established as the first-choice centre-back pairing at White Hart Lane, Maguire could struggle to get playing time if he decides to move to north London.
"I want to play week in, week out," he said earlier in May. "I set myself a target to play week in, week out in the Premier League.