Those two players are Jake O'Brien and Davinson Sanchez. These centre-backs are apparently on the market and could be of interest to Everton.
O'Brien and Sanchez have previously been the subject of stories that the Toffees are keen to bring in one or other of these players.
Everton have moved quickly to strengthen their forward options as a priority in the early days of this current transfer window.
Jack Harrison returning on loan again, Iliman Ndiaye permanently and now possibly Jesper Lindstrom have joined, or are about to, hopefully giving Sean Dyche some needed additional firepower up front.
At the same time. rumours have constantly circulated that Jarrad Branthwaite would leave for Manchester United. but so far nothing has happened and it now seems that the Blues might well keep him.
However, Ben Godfrey has left the club for Atalanta and even if Branthwaite stays, the Toffees will only have him, James Tarkowski and Micheal Keane as centre-back options.
Of the two players mentioned above, while Sanchez might be the easier to sign, O'Brien looks the best bet.
The Irishman is young and has just enjoyed a very solid season in France with Lyon after leaving Everton's Premier League rivals Crystal Palace.
But there are a number of other clubs said to be interested in the 23-year-old defender. The latest possible suitors are Dutch giants Ajax.
That competition and the possible fee involved in signing him will probably make any move by the Blues very unlikely.
This is also particularly the case after last week's news that The Friedkin Group have pulled out of their proposed takeover of Everton.
So Sanchez could be the player who is a more affordable option - and he has supposedly invited Premier League clubs to come for him - although there are other central defenders out there on the market.
He has plenty of English top flight and international experience, and has just played in the Copa America final against Argentina.
Everton have been surprisingly active in the transfer market and despite the takeover failing, that looks likely to continue.