Former Everton midfielder Steven Pienaar training with Sunderland
The 34-year-old midfielder - who has been linked with a move to Orlando Pirates - was released in the summer after just half a dozen appearances last season for the Toffees.
The former Ajax, Borussia Dortmund and Tottenham Hotspur midfielder is training with Sunderland at the club's Academy of Light base.
After succeeding Sam Allardyce midway through the pre-season campaign, Moyes admits time restraints have left him with little chance to see all of his potential new recruits in the flesh, with less than a fortnight until the Premier League gets underway.
But the ex-Manchester United boss hopes to counter that obstacle by bringing in homegrown players, or at least those who have experience of competing in English football.
Pienaar would certainly fit into that mould, with the South African international boasting a wealth of top flight experience.
Moyes said: "We want to get it right, so it’s important that we get people who know the Premier League and how it works.
"I would always go and watch the players, see them live, but that’s impossible.
"My style wouldn’t be to take anything off a video, but unfortunately with some of them at the moment, I’m having to do that.
"I’m trying to avoid that situation as much as possible, because if you get into it too much, you can make mistakes.
"I’ve never been off the telephone, I’ve done an awful lot of work just trying to find out who could be available and what could happen.
"We’ve got a couple of offers in for players just now, written offers, and we are just waiting for them to come back."