Sources close to the Formula One team indicated the reports were accurate.
A McLaren spokesman said no deal had been signed with any driver for 2014, other than 2009 world champion Jenson Button.
Magnussen, 21, is the son of former McLaren and Stewart grand prix driver Jan Magnussen and won the Formula Renault 3.5 series this year.
The BBC and autosport.com websites both reported McLaren had decided to give Magnussen the drive.
Team principal Martin Whitmarsh earlier told reporters that talks were still ongoing for the second seat at the former championship-winning team.
"There has been a lot of honest feedback both ways, which is best done in private not in public. We'll see in the future," he said ahead of this weekend's U.S. Grand Prix in Austin, Texas.
If Magnussen is confirmed in the seat, he will be McLaren's first rookie driver since Britain's Lewis Hamilton made a sensational debut in 2007. He won the title the following season.
Last month Whitmarsh described Magnussen, who is a McLaren development driver, as "pretty special" and "lightning quick".
Perez joined McLaren from Sauber at the end of last season after Hamilton left for Mercedes and has struggled with an uncompetitive car.
The 23-year-old Mexican has scored 35 points to Button's 60 in 17 races.
Before this month's Abu Dhabi race it had seemed that Perez was set to be confirmed, with Whitmarsh indicating as much, but the feeling changed after a disappointing performance under the Yas Marina floodlights.
"Abu Dhabi was difficult. It was not the result he and we wanted but difficult weekends happen," said Whitmarsh.
"In an era of change you need bright drivers. I think Sergio is a clever guy and I think in that regard he's a good driver for anyone next year, including ourselves.
"I think we've got two intelligent drivers now and I'm sure we'll have just that next year."
(Reporting by Alan Baldwin, editing by Tony Goodson)
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