Is there a way to know how many of currently unconfirmed transactions in the MemPool is currently being attempted by other miners?

No one cares

(about what other miners are exactly working on)

Miners have no way of knowing the contents of block templates being used by other independent miners.

There is nothing in the Bitcoin network protocol that provides for miners to share what they are up to. Considering the speed at which miners must vary block templates, I imagine doing so would be infeasible or at least waste huge resources somewhat pointlessly.

The contents of those other block templates is of no interest. As soon as one miner publishes a valid block all other miners must abandon their work and restart mining regardless of what is in anyone's block templates.

Don't knowingly buy expired lottery tickets

(unless you have the resources to persuade the whole world the prior winner is unworthy?)

Continuing to work on a block template that includes a transaction that has already been confirmed would be pointless but, more importantly, The active blockchain is linear. Miners must always work on a block template that links back to the current head block. As soon as a new head appears on the active chain, miners must use it regardless whether the block is empty¹ or not, whether it contains transactions they had been working on or not.

Ultimately there can only be one block at any height n in the active chain. It is generally likely to be unproductive and wasteful to knowingly continue working to produce a second block at the same height as one you know about. The purpose of Blockchain reorganisations is to ensure that ultimately all Bitcoin nodes agree which chain is the active chain and therefore all agree exactly which block occurs at each height n.

Poolside chatter

Miners working in a pool are subject to some form of coordination but I believe the description above remains valid more generally.

See also

Notes

1. Containing no transactions other than the miner's coinbase transaction.

You can get bonuses upto $100 FREE BONUS when you:
💰 Install these recommended apps:
💲 SocialGood - 100% Crypto Back on Everyday Shopping
💲 xPortal - The DeFi For The Next Billion
💲 CryptoTab Browser - Lightweight, fast, and ready to mine!
💰 Register on these recommended exchanges:
🟡 Binance🟡 Bitfinex🟡 Bitmart🟡 Bittrex🟡 Bitget
🟡 CoinEx🟡 Crypto.com🟡 Gate.io🟡 Huobi🟡 Kucoin.