Paul Lambert looked to be closing in on his second signing of the summer after Millwall accepted a bid for striker Steve Morison.

After a day of claim and counter claim in south London, the Lions confirmed on Thursday afternoon that they had accepted an increased bid – City's fourth and reportedly over the �2m mark – and that they had granted permission for Morison to talk to the Canaries.

'We have allowed Steve to talk to a Premiership club having negotiated a deal that has matched our valuation,' said Lions chief executive Andy Ambler. 'It is now for Norwich and Steve to agree terms.'

A statement on the City website said: 'City can confirm they have agreed terms with Millwall for Lions' striker Steve Morison. Millwall have granted permission for the Canaries to speak to Morison. However, any deal is subject to a medical.'

Morison's name had been on the radar for some time – as far back as the January transfer window – but it was the player himself who brought it to the fore last week when he put in a written transfer request, having revealed that Norwich had had bids rejected.

'Norwich have made a couple of bids that have been turned down so I've done what I've done,' Morison said at the time. 'I want to play in the Premier League, I might not get another opportunity.'

City reportedly refused to give up their pursuit of the 27-year-old Wales international, who has scored 40 goals in two seasons at Millwall since signing from Stevenage in 2009, and yesterday morning a south London newspaper claimed agreement was imminent, only for the Lions to quickly respond with a statement which said: 'Contrary to media speculation, we would like to confirm that at present Millwall have not accepted a bid for striker Steve Morison.'

However, just before 5pm yesterday, confirmation came through that attempt number four had succeeded – paving the way for City to talk to the 6ft 2in front-man, who would add to front-line options that already include skipper Grant Holt, Simeon Jackson, Chris Martin, Aaron Wilbraham, Oli Johnson, Cody McDonald and new boy James Vaughan.

Lambert unveiled Vaughan at a press conference on Tuesday, when he refused to talk specifically about Morison.

'Until they come in there is no point in me speaking about it,' he said.

'I never read much into rumours or speculation – until they actually come through the door and we have got them that's the time to comment on it.

'It's is like the (Miroslav) Klose rumour – that was just ridiculous.'