He was sacked by PSG last month, however, after allowing the Ligue 1 giants to drift into a title race – with Mauricio Pochettino since appointed his successor.
Tuchel previously held talks with the Chelsea hierarchy back in 2018 but, after choosing to head to PSG instead, the Blues ended up swooping for Maurizio Sarri.
Allegri is another contender for the job, having been out of work since leaving Juventus back in 2019.
And Hasenhuttl has his admirers at Stamford Bridge having worked wonders at Southampton, helping them to ninth in the table.
Chelsea know it will be difficult to part ways with Lampard, who is widely considered one of the best-ever players to feature for the club.