French outlet Le10 Sport claim the Ukraine boss, who failed to hit the heights at Stamford Bridge as a player, is on a list of targets being discussed by the Blues hierarchy.
Shevchenko native country qualified for Euro 2020, which has been postponed until this summer, finishing their group unbeaten and ahead of holders Portugal.
And the former AC Milan striker has another link with Chelsea these days, given that his 14-year-old son Kristian plays for the club's academy.
Shevchenko has been manager of Ukraine since 2016 but has not held any other managerial positions.
His stint at Chelsea as a player came between 2006 and 2008, where he played alongside current boss Frank Lampard.
The pressure is on Lampard at present after his team were comfortably beaten 3-1 at Stamford Bridge by Manchester City at the weekend.
Fans continue to back the club hero.
But reports immediately after Sunday's defeat pointed to Abramovich looking at alternative options.
"I'm not worried about my future or relaxed about whether we may have highs or lows. I just told the players about it," Lampard said.
"I was expecting difficult times this year.
"I know it's not that simple. I know where we are. Whether it puts pressure on me or not, it doesn't matter.
"A month ago, everyone was asking me if I was going to sign a new contract, now people are going to say different things because suddenly we are having a bad time where we have lost four matches.
"So the pressure remains constant in this business and you know that there will always be difficult times ”.
Lampard had his squad bolstered by over £200m worth of talent in the summer window.