Bristol Rovers' Lambert is a target for Huddersfield
The Pirates' League One rivals were one of a clutch of clubs who expressed an interest in the marksman during the January transfer window, only to be rebuffed.
But now the Yorkshire club are understood to be renewing their interest with a £750,000 bid thought to be in the offing.
The Terriers are in the market for a top goalscorer after veteran striker Andy Booth retired at the weekend, rounding off his second spell at the club with a goal in their 1-1 draw against Leyton Orient.
Bristol Rovers are expecting another flurry of interest in Lambert over the summer after he netted in their 4-1 weekend win over Hartlepool, taking his goals tally for the season to 29 – which saw him finish level with Swindon's Simon Cox in the race to finish as League One's top marksman.
Lambert, who is still under contract with Rovers, has made no secret of his desire to play in the Championship but says he is open-minded about the prospect of joining another League One outfit.
"Obviously I want to play in the Championship if the right offer comes along – I think everyone would accept it's the right decision for me," he said.
"But I've loved being here and the fans have made me feel welcome from the moment I arrived, so if nothing happens I'll be happy to be here next season.
"If someone put an offer in from League One and it got accepted, then I don't know. There are a lot of good clubs in League One so I wouldn't rule it out, but I want to play in the Championship. I want to play as high as I can and I think I'm coming to my peak years now.
"I think I can make the step up – it just needs someone to take a chance on me and spend some money.
"But until something happens I'm a Bristol Rovers player and I'll just carry on doing my best."
Bristol Rovers' boss Paul Trollope, pictured, refused to discuss speculation about Lambert's future, although he has already made plain his desire to hang on to his main goalscorer.
"He's joint leading scorer in the division and he's had a fantastic year. He was our leading scorer last year too and his form has been impressive. He has led the line well for us and become pivotal to how we do things," he said.
The coach was happy with the way his side rounded off the campaign to finish in 11th place.
"It was pleasing to score four goals at home again – that's 79 for the season, which is a fantastic return," said Trollope.
"It maybe highlights a few deficiencies in other areas. But for those, it may have been a different story this season.
"But it gives us something to build on for next season and we'll be hoping to continue scoring goals while improving other aspects of our game.
"I said I wanted us to finish in the top half of the table and I think we have deserved to do that because we have worked very hard. To finish on a winning note is pleasing.
"There were still things I wasn't happy with. I would have liked us to have kept the ball better in the second half when we were 4-1 up – it's at times like that you should enjoy your football.
"But by then the job was done so maybe you could understand a bit of tiredness and laxity creeping in.
"The effort and commitment from the players has been good all year and it's very rarely that I have seen a lack of desire. To finish 10 points better off than the previous season shows progress."
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