Lord Timpson said the south-west London prison had been given the "green light" to use artificial intelligence after a specialised team was sent in to find "some quick fixes".
A double manhunt was launched following the incorrect releases of an Algerian sex offender and a fraudster from the prison.
Brahim Kaddour-Cherif, 24, was mistakenly freed on October 29 before being arrested on Friday after a police search.
He was serving a sentence for trespass with intent to steal, but had previously been convicted for indecent exposure.
He is understood to have overstayed his visitor's visa to the UK after arriving in 2019, and was in the process of being deported.
Another prisoner, Billy Smith, 35, who was accidentally freed from Wandsworth on Monday – after having been sentenced to 45 months for multiple fraud offences – handed himself back in on Thursday.
Responding to questions in the upper chamber on Monday, Lord Timpson said: "The number of releases per prison varies dramatically.
"In HMP Gartree, they average two releases a year, whereas, as I previously said, in Wandsworth, it is 2,000.
"But that is why the digital team last week went into HMP Wandsworth to look at what are the opportunities for some quick fixes to embrace digital technology.
"We had the AI team that went in and to give you a couple of examples – they think an AI chatbot would be really helpful, and also a cross referencing for aliases, because we know some offenders have more than 20 aliases.
"So it is examples like that, and we've given them, we've given the team, the green light to get on with that."
