Blues owner Abramovich is currently unable to enter the UK after problems gaining a visa, but that is not stopping him pressing ahead with a summer of changes at Stamford Bridge.
The club have yet to make a decision on the future of Antonio Conte as manager, with the Italian set to leave after despite delivering a Premier League and an FA Cup in his two years in charge.
But despite uncertainty over who will be the boss next season, Abramovich and his advisers are clear they need to fund wholesale changes – and it is £100m Bayern Munich star Lewandowski who is their top target.
Chelsea have already made moves to press ahead with a transfer window bid to land the Polish international forward.
Lewandwoski, 29, has signalled he wants to leave the Bundesliga giants this summer to take on a new challenge in another country – and as SunSport revealed last week, he met with new agent Pini Zahavi to discuss his next move.
There is no shortage of clubs interested in landing the forward, who has been one of the most prolific in Europe over the past six years.
But the two clubs with most hope of securing his signature are Chelsea and European champions Real Madrid.
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Lewandowski has openly admitted in the past he would love the chance to make a move to the Bernabeu.
And Real have offered encouragement that they will be interested in a deal this summer as Zinedine Zidane looks to overhaul the frontline at his disposal.
But the £100m Bayern are said to want for a player who turns 30 in August is understood to be causing some concern in Spain.
That is not a problem for Chelsea, who believe Lewandowski is the man who can solve their goalscoring problems next season.
Alvaro Morata has not enjoyed the impact hoped for at Stamford Bridge, and the Blues finished the season with January capture Olivier Giroud as their number one striker.
Abramovich is aware Eden Hazard wants to see top class players arrive over the close season before he decides whether to commit his long-term future to the club.
If he could land one of the game's best forwards that would go a long way to proving to Hazard that Chelsea are serious about remaining as genuine title challengers.
It would also mean the Blues finally have a cutting edge to their attack missing since Diego Costa was dumped by Conte last summer.
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