Barry was seen entering the Everton training ground with a little more than 20 minutes remaining until the 11pm deadline ahead of a potential move to Goodison Park.
The 32-year-old England international is currently thought to be in talks with the Toffees after they came to a compromise with Manchester City over a fee for the midfielder.
City were reportedly holding out for an upfront bid for the player, while Everton were keen on a loan deal with a view to a permanent transfer in the future.
It now appears that the two clubs have agreed a deal and Barry is now believed to be discussing personal terms.
Barry would become the Toffees' first signing on this season's deadline day.