According to the Daily Mail, the broadcasting watchdog has so far received 374 complaints over the plot, which has seen Ronnie Branning lose her baby son to cot death before swapping him with Kat Moon's (Jessie Wallace) child in her grief-stricken state.
However, in a statement, a spokesperson for the regulator said: "We assess whether programmes have gone against the Broadcasting Code. At the moment, we don't think that's the case. The clause it might go against would be 'general harm and offence'."
The representative added that Ofcom will wait until the storyline is over before making a final decision over whether action will be taken.
In addition to the Ofcom complaints, it has been confirmed that over 3,400 people have contacted the BBC directly to raise concerns over the storyline.
However, an official statement released by the corporation has defended the plot and revealed that "viewers will see the situation resolve itself over the coming months".
In a separate development, the BBC has today confirmed that Samantha Womack - who plays Ronnie - is to leave EastEnders this year. Tabloid reports have suggested that she is unhappy over the nature of her current storyline.