BTA said Stoichkov, who has never coached a club in his native country, had agreed a deal with Litex and was expected to arrive in Lovech on Friday.
The club, however, have refused to comment on possible changes.
Stoichkov, who turns 46 next month, was a key member of Barcelona's 'Dream Team' that won the Spanish title four times in succession in the early 1990s under Dutch coach Johan Cruyff.
The striker also helped Barca win their first European Cup in 1992.
Stoichkov's goals led Bulgaria to the semi-finals of the 1994 World Cup and he is recognised as one of the country's greatest sportsmen.
Litex, who have won the league for the past two seasons, named Dzhambazki as coach in October after Luboslav Penev left to take over the national team.
Dzhambazki's side have managed one win and one draw in four matches and are seventh in the table at the mid-season break, 11 points behind surprise leaders Ludogorets.
'The Dagger', as Stoichkov is known in Bulgaria, has been unable to match his playing achievements during his time as a coach.
A three-year spell in charge of Bulgaria ended in failure to reach the 2006 World Cup finals and he then left Spanish club Celta Vigo within a few months of taking the job.
In 2009 he joined South African club Mamelodi Sundowns and led them to second place in the league but resigned at the end of the season after failing to win a contract extension.
Stoichkov, who in 1994 became the only Bulgarian to be named European Footballer of the Year, has recently worked as an adviser for top-flight Russian club Rostov.
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.