The Swans have completed the formalities on the signings of Rory Donnelly and Darnel Situ and are hopeful that McEachran will be next.
Donnelly, 19, had already penned a three-and-a-half-year contract to join the south Wales club from Cliftonville for an undisclosed fee when the transfer window opened, and he has now received international clearance to play a part in Swansea's Premier League campaign.
Swansea, who confirmed the news on their official website, had attempted to sign France Under-19 defender Situ from Lens for £250,000 at the end of the summer transfer window, but FIFA refused to give international clearance for the move at the time.
Situ has spent the intervening period training with Swansea and is now eligible to play after also receiving clearance to join on a two-year deal.
Manager Brendan Rodgers has also brought Hoffenheim midfielder Gylfi Sigurdsson in on loan until the end of the season, and is close to reaching agreement for McEachran to move to the Liberty Stadium in a similar switch.
Rodgers, formerly a youth and reserve team coach at Stamford Bridge, has previously stated his admiration for the player, and his belief that the 18-year-old would benefit from a spell with Swansea.
And it looks as though the Swans are close to seeing off reported interest from the likes of Aston Villa to bring in the England Under-21 international.
Rodgers told talkSPORT: "Hopefully, we can get that agreement confirmed in the next 24-48 hours. We've obviously made an enquiry.
"Josh is a boy I know well so we'll see if we can organise the move over the next few days.
"He'll be brilliant for the Swansea supporters and they'll get to witness one of the best talents this country's got.
"He's a player who sees passes from the sky. He's an incredible passer of the ball and I know the England set-up have very high hopes for him as well.
"He's a kid who can create chances and has wonderful vision on the ball - he fits perfectly into our team.
"I've got a really talented group of players at this level and he'll come into the squad and add to that for the second part of the season."
McEachran had posted on his Twitter page: "Hello tweeps. I'm still not 100 per cent sure on the loan deal. When I am, I'll let you all know."
Rodgers had said last week that he could only see himself making one further addition to his squad during January, but he has been linked with making a cash-plus-player bid for Bristol City forward Nicky Maynard, with Stephen Dobbie mooted as being part of the exchange.
The Swans have also released Greece centre-half Vangelis Moras after his three-month deal expired.
