Academy product Henderson helped Sheffield win promotion from the Championship last season and has kept 10 clean sheets for them in the Premier League in the current campaign, second only to Burnley's Nick Pope.
With David de Gea currently the first choice in Manchester, Solskjaer said no decision had been made where the 23-year-old Henderson would play next season.
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"Dean has made some great choices over the years and has developed fantastically," Solskjaer said ahead of the Premier League's restart on Wednesday following a coronavirus shutdown.
"This season has proved a great experience for him, he's done himself some favours with his performances and proved he will be England's No. 1 and Man United's No. 1 at some point."
Manchester United, who are fifth in the league on 45 points, face Tottenham Hotspur on Friday. The Blades resume their campaign at relegation-threatened Aston Villa on Wednesday.
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