Jose Mourinho's competitive spirit means the answer is likely to be yes.
Despite assertions that Chelsea have a full complement of strikers and do not need to sign another one; the opposite is true.
Samuel Eto'o is underperforming and Demba Ba is just killing time before being moved on in January, opening up a striking spot - even with Romelu Lukaku due to return to the first team next season, if the opportunity to sign a top player came about, you can be sure Chelsea would try to take it.
Arsenal were put forward by a Spanish newspaper last week as Dortmund striker Lewandowski's most likely Premier League destination, and with the Gunners a striker short, it's logical Arsene Wenger could try to tempt him to the Emirates.
The problem for the Gunners is, any move to do so is likely to be met with resistance by Mourinho. Chelsea need him far less than Arsenal do, but they would likely go all out to stop Arsenal getting him just to make a point.
The Chelsea boss confirmed he did not sanction the loan of Demba Ba to Arsenal because he feared along with their acquisition of Mesut Ozil, they would be too strong, and even more of a title threat than they are at present.
You can only imagine how fearful he would be if they had the prolific Polish striker in their weaponry, the man who scored four goals in one game to destroy his Champions League challenge with Real Madrid at the semi-final stage last season.
And then there is the way Mourinho oversaw Chelsea hijacking Tottenham's move to sign Brazilian playmaker Willian in the summer, again fearful of a rival strengthening, willing to complicate his own squad options just to stop a rival in their tracks.
There were also unverified reports in Spain, that Mourinho even enquired at the last minute to try and steal Ozil from Arsenal's grasp, but in this case was unsuccessful.
It's gamesmanship of the highest order, but Chelsea can afford to do it. Lewandowski's transfer status is unclear in that Dortmund have yet to indicate whether they are actively trying to sell rather than let his contract expire in the summer, but if one London club in red and white make a bid, expect the one in blue to try and top them.
Arsenal fans, are you worried Chelsea could stop the dream transfer?
image: © Roger Gorączniak