Blockchain.info is quite not a better wallet for bitcoin enthusiasts, but recommended too, for its user friendly site and App. To your question, private keys can be generated on Blockchain.info through Electrum, first you will have to get a backup phrase on your blockchain wallet. Click settings> Security> backup recovery phrase. Write it down then go Electrum click new/restore> next> choose standard as option> Then click, I already have a seed, insert the recovery phrase you got from Blockchain.info, you can decide a password for your wallet then click the wallet option then choose the wallet you want, right click and select private key.
We all know how relevant our private key is, your private key is your funds keep them safe. Someone who has your private key can import them to any wallet and move all your money.