Frank Lampard has given the clearest indication yet that Olivier Giroud could leave Chelsea this month, with Inter Milan pushing to sign the France striker.

The Blues boss has admitted for the first time that Chelsea do not necessarily need to sign a replacement for Giroud to leave Stamford Bridge in the January transfer window.

Giroud’s agent is understood to have agreed personal terms with Inter, with ex-Chelsea boss Antonio Conte keen to recruit the World Cup winner, but Lampard insisted no deal has yet been struck.

Asked if Chelsea need to recruit a replacement before Giroud can leave, Lampard said: ‘Not necessarily.

‘With Ollie the situation is, if it’s right for everybody, and first and foremost that’s us as the club, then we’ll look at whether he can leave the club.

‘He’s been a great professional here, who has continued to train professionally without many opportunities. But I still have to make a decision for the football club, and nothing’s done yet.

‘Everyone’s talking about it so I’m not going to beat around the bush. I think his agent has spoken to the club, but until anything’s done he’s a Chelsea player.’

Allowing Giroud to move to Inter without recruiting a replacement would leave Chelsea with Tammy Abraham and Michy Batshuayi as the only recognised senior strikers.

The Blues have been heavily linked with a move for Lyon forward Moussa Dembele, but Lampard insisted Chelsea have not seriously discussed a deal for the ex-Celtic player.

And Lampard revealed Chelsea are not yet on the verge of completing any transfers this month.

Asked about Dembele, Lampard said: ‘He’s a player I know and a player the club know, but I’m surprised to see his name crop up so frequently in relation to us, to be brutally honest.

‘And I could say the same thing about a number of players this week. I don’t want to go cut and dried on anyone. But it’s not one we’re openly talking about.’

On whether Chelsea are close to finalising any signings, Lampard added: ‘No, not at the moment. But what is close? It’s January, and if it’s right we’ll look at it.

‘Nothing’s imminent, we’re not going to have any big news today, or tomorrow.’