The Bank said De La Rue and Innovia Security, which produced the £5 and £10 plastic banknotes, had a "high degree of confidence" that the oil could be used in the plastic £20 note, which will be introduced in 2020.
Environmentalists have warned that palm plantations destroy forests and other valuable ecosystems, accounting for 8pc of global deforestation between 1990 and 2008.
However, the Bank said using coconut oil, also identified as a suitable substitute, would require "more land to produce the same volume of oil".
The Bank has said it will not withdraw the current plastic £5 note, which was introduced last year. The new plastic £10 note this September will also contain tallow as 275m notes have already been printed.
The Bank expects to print around five billion polymer £20 notes over 10 years.
It said the palm oil needed to produce the notes could be sourced "from one year's production of less than six hectares of palm oil plantation".
In 2013, there were around 12 million hectares of palm in Malaysia and Indonesia alone, it said.
Using animal fat would "equate to the usage of tallow by-products from around 25-30 cattle".
Emma Keller, agriculture commodities manager at the WWF, welcomed the "thorough and extensive review" conducted by the Bank, including a detailed report by the Experts in Sustainable Forest & Agricultural Advice (Efeca).
However, she stressed that growing demand for palm oil came at the "expense of human rights and tropical forest", and that the organisation would only support oil where production could be traced and certified by the Roundtable on Sustainable Palm Oil (RPSO).
"People don't want the bank notes in their pocket to come with such a high environmental cost," she said. "The bank must only source RSPO certified sustainable palm oil or none at all."
The Bank's consultation closes on May 12.