But Giroud has insisted those rumours are false and revealed he was baffled to receive messages about the potential transfer.
‘Italians, they get carried away quickly,’ Giroud told Telefoot when asked about the speculation.
‘I was surprised to receive messages from friends this morning telling me about this rumour.
‘That’s far from being the case. I am a Chelsea player and I feel good here.
‘I didn’t have the great end of the season that I did to leave like this, and not believe in my chances. I will fight for my place.
‘But it’s always good to get the attention of these kinds of clubs, it’s flattering. But I remain focused on Chelsea.
‘We will see what will happen in the coming weeks. But there is nothing signed or done. I prefer to deny it.’
Giroud played second fiddle to Tammy Abraham last season and will face even more competition for a starting place in the coming campaign after Chelsea spent big to land Werner from RB Leipzig.
‘The coach can evolve,’ Giroud said. ‘It is not stuck in one tactical system.
‘Werner brings us another string to our bow.
‘He has different qualities to mine, so that makes me think that’s not such a bad thing. We could complement each other.
‘I hope that I can continue the momentum I have had. I have high hopes for the future.
‘We will see how it goes over the next few weeks. I’m impatient anyway.’