The Telegraph reported that players would be given permission to compete in the lucrative Twenty20 competition.
But Strauss, 38, said: "I can't foresee any circumstances in which we would weaken our Test team in order to allow a player to play in the IPL or any other franchise-based competition."
The IPL takes place in April and May.
England play Sri Lanka in two Tests in May 2016, their first action of the domestic summer.
Strauss told BBC Test Match Special on Wednesday that "more separation" of the Test and one-day teams will improve their chances of winning the World Cup.
Asked about the IPL and the Big Bash, Australia's Twenty20 tournament, he said: "I'm a massive fan.
"If you are an overseas player, what those Twenty20 competitions do is put you under real pressure. You have to stand up and deliver."
England players, including current ODI captain Eoin Morgan, have competed in the IPL, although they have never missed Tests to do so.
Strauss has returned to the UK from the United Arab Emirates, where England lost the first game in the four-match one-day series against Pakistan.
One man quick to air his views on the subject was former England batsman Kevin Pietersen, who found himself at odds with the England and Wales Cricket Board over his desire to play in the IPL and commented on Twitter about the developments.
"With this decision now, the whole situation is proving to be personal!" he wrote.
"[Eoin] Morgan missed an international this year as captain! Missing any Eng cricket for IPL is what I'm on about! Such hypocrisy!"
Pietersen was told by Strauss in May that he would not be part of the team's plans for the summer because there was a "massive trust issue".
The South African-born batsman was instead offered an advisory role with the England one-day team, but rejected the opportunity.
He referred to that offer on Friday when he added: "Why should I advise when I'm still good enough to walk into any England side if there wasn't personal grudges?!"
England players will not be allowed to miss Test matches to play in the Indian Premier League, says director of cricket Andrew Strauss.