Reports have suggested the Parkhead club are keen on Sunderland hitman Fletcher and Watford winger Anya.
But Hoops assistant boss John Collins confirmed Ronny Deila will not be able to cover Fletcher’s £45,000 a week wages.
Anya, now on top-flight terms after the Hornets’ promotion to the Barclays Premier League, is also earning too much to make him a realistic target, according to Collins.
Speaking at Edinburgh Castle following the release of the 2015/16 Ladbrokes Scottish Premiership fixtures, Deila’s number two said: “I don’t think I can say they’re players that we’re trying to sign.
“They’re two good football players who I admire but they’re both Premiership players so the reality is they’ll be on Premiership wages, so probably out of our wage bracket.”
Collins also confirmed the path was clear for Rangers to re-sign Danny Wilson from Hearts after revealing Deila “won’t be pursuing” the 23-year-old defender.
However, the former Scotland midfielder is confident Celtic will not need to find a replacement for Virgil van Dijk.
The Dutch centre-back hinted last week that he was ready to make a move away from Glasgow two years after signing from FC Groningen.
But Collins said: “I’m in regular contact with Virgil and I know for a fact that he is very happy at Celtic.
“He’s enjoying playing and enjoying training and he has got two years to go [on his contract]. There may come a time when Virgil moves on but at this moment in time he is our player.
“We’re enjoying having him and I do think he will be a Celtic player come the first day of the season.
“When you have two years to go on your contract, the club are always going to be the one who makes the decision on whether they sell you.
“But we want him to be happy, of course, as well.”
So far Celtic - who will open their Premiership campaign at home to Ross County on August 1 - have made just one summer signing after landing Belgian defender Dedryck Boyata from Manchester City.
Collins is hopeful more will arrive by the time the Hoops kick-off their Champions League qualifying bid on July 14 or 15 - but admitted it could take the club time to find the right targets.
“It’s never easy,” he said. “We’ve got good players but I think the important thing is to try and sign players who are going to make you better.
“But with the money there is in England, France, Spain and Germany, we can’t compete with these teams when it comes to buying players.
“So we have got to take our time and try and get the ones who nobody else has spotted.
“We don’t have the television money that you get in these other countries but we are still a massive football club with a great support, a great stadium and a great atmosphere in that stadium.
“So we are still an attraction for a lot of players. When players come to Celtic Park, they always enjoy it. It’s a special place.