French Ligue 1 giants’ Olympique de Marseille, Olympique Lyonnais and Paris Saint-Germain are also reportedly keeping tabs on the Cameroon international.
Bedimo, 28, would like to play UEFA Champions League football next season, having started five of La Paillade’s six European encounters this term.
The 28-year-old left-back is believed to be valued at around £5 million by Montpellier.
“I have heard of the interest of clubs in the Premier League, but when you hear there is interest from a Champions League club in France then you have to think about it,” said Bedimo.
“Newcastle and West Ham are both good clubs in the best league in the world, but I will not decide my future until at the end of the season.
“I want to be playing in the Champions League as well.”
Bedimo has featured in 25 league matches, 22 starts, for Montpellier — who are currently in seventh-place in the Ligue 1 table — this season.
Only Daniel Congre, Hilton, John Utaka and highly-rated No. 10 Younés Belhanda have started more league fixtures than Bedimo in 2012-13.
Bangna agrees new Fulham deal
Former Chelsea winger Buomesca Tue Na Bangna has signed a new three-year deal at Fulham, which will keep him at Craven Cottage until the summer of 2016, according to Sky Sports.
Bangna, 19, joined Fulham from Chelsea in August 2011.
The Guinea-Bissau-born Portuguese youth international impressed while on first-team duty in the summer, only to miss the first half of the current campaign with a knee injury.
Fulham boss Martin Jol tipped the youngster to have a breakthrough 2012-13 campaign after a series of fine performances in Development Squad and Under-18 matches for the Cottagers last season.
Unfortunately, the 19-year-old winger endured a frustrating, injury-ridden season, but is finally fit again and happy with life in southwest London.
“It’s nice to hear that the manager rates me,” said Bangna. “I think he likes the way I play but I need to keep working hard and trying to impress him. He’s given me a lot of confidence.
“I feel much better, I feel fit. It was very frustrating to be injured. I’m a young player and I was involved with the first team in pre-season and had done well, but then picked up this injury. But everything is good now.
“I went with the squad to Newcastle (for Sunday’s Premier League game) which was a good experience for me. I didn’t get on the bench but hopefully I will in the future.
“I’d love to play before the end of the season but we will have to see. If I’m given the opportunity I will take it. I’m ready if the manager wants me.”
Fulham, currently in 10th-place in the league table, are currently eight points clear of the relegation zone.
Expect Martin Jol to give Bangna, who has the qualities — youth and pace — that the Cottagers are thoroughly lacking, his Premier League debut before the end of the season.