Olivier Giroud has scored 13 goals from 29 Premier League starts this season. He has six from another 13 appearances in assorted cup competitions. Nineteen goals from 42 appearances is a perfectly respectable record, and he is Arsenal's top scorer (with Aaron Ramsey next on the list with 13).
However, that Giroud is Arsenal's unquestioned first choice for centre-forward is perhaps a symbol of why they will not win the Premier League this season. Indeed, if this continues to be the case, it is doubtful that they will ever win the title.
Of the 13 league goals Giroud has scored, none have come against the rest of the top four. Only one, the winner against Tottenham back in September, has been scored against a team in the top six. He didn't even manage a goal in two games against Manchester United. Perhaps not coincidentally, Arsenal have the lowest goals total (55) in the top four.
Of course, a team can mount a convincing title challenge without having a top-class centre-forward, as Chelsea are currently demonstrating. But Jose Mourinho's side can get away with that because it has the best defence in the league, and it gathers goals from different sources—37 from midfielders of various descriptions, for example.
The rumours about Olivier are not surprising given that he is having a great season.
Juve were interested, it is true, but that was before he moved to Arsenal. He's very settled in London and the club is happy with him. I think there is no possibility he might change club. At the end of the season we will meet with the Gunners to discuss a contract extension.
The fact remains that Giroud is too wasteful to be a reliable striker for a team challenging for a title. He would be a perfectly decent back-up for a side with Arsenal's apparent ambitions, but he shouldn't be the only option for Arsene Wenger.
It's perfectly possible that Giroud is tired this season, something Arsene Wenger admitted in January (per Arsenal's official website). Giroud may also have been distracted in February after allegations about his private life appeared in papers like the Daily Mail.
The purchase of Mesut Ozil last summer suggests that Arsenal have the means and the intent to pay top prices for top talent, be that Julian Draxler, Karim Benzema or any of the other names linked to them in the press (per the London Evening Standard).
There are obviously other reasons for Arsenal's surrender in the title race: their questionable mentality, a lack of a physical presence in midfield, injuries and so on and so forth. One also has to question Wenger's managerial skills and methods, but that's an argument for another time.
This isn't a silver bullet, but Arsenal need someone better than Giroud leading their attack if they are to have a chance of challenging successfully for the Premier League title.