Abraham, 21, scored his first goals for the club in Saturday’s 3-2 victory over Norwich at Carrow Road.
Despite impressing for Villa and now Chelsea, Redknapp says Abraham is ‘not the finished article’ and has urged him to ‘master the dark arts’ like former Blues star Costa.
Spain international Costa scored 59 goals in 120 appearances for Chelsea, helping the club win two Premier League titles in his three-year stint at Stamford Bridge.
Redknapp told the Daily Mail: ‘Let’s give Frank Lampard credit for the way he secured his first Premier League win as a manager at Norwich.
‘There was pressure on his side to win but Lampard had the courage to start with Tammy Abraham up front and his bravery was rewarded as the 21-year-old got two goals.
‘Abraham is not the finished article. I think he needs to be nastier and a master of the dark arts like Diego Costa. Then maybe the No 9 shirt will be his for the foreseeable future.’
Abraham, meanwhile, has revealed why he sprinted over to the touchline to celebrate with Lampard after putting Chelsea in front against Norwich.
‘It’s always nice to have that support behind you, especially how he supports the young lads,’ the forward said.
‘He gives us confidence. When a coach believes in you, you just want to do your best and give 100 per cent.’
Chelsea face Premier League new-boys Sheffield United at Stamford Bridge on Saturday.