Sky News reported that Tesco chief executive Dave Lewis had approved the appointment of investment banker Greenhill to work on the sale of Dobbies.
Tesco has decided that non-core businesses including Harris & Hoole coffee shops, Euphorium bakery, Giraffe restaurants and Nutricentre will be sold, Sky added.
Lewis is likely to announce his plans for them when the company unveils its full-year results on 13 April, according to insiders. He said last October he was not going to sell Dobbies.
Tesco bought Dobbies in 2008, and built the chain to 35 garden centres. Dobbies recorded a £48m loss in its 2014-15 financial year after writing down the value of its real estate.
A Tesco spokesman said the company did not comment on "rumour and speculation".
However analyst Freddie George of Cantor Fitzgerald said news of the sale was "more than a rumour". Wyevale Garden Centres owner Terra Firma is most likely to buy Dobbies, though another private equity firm might take it on, as might former industry heavyweights James Barnes or Nicholas Marshall.
See more in Horticulture Week 15 April.