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?!"

The three sides will play two matches apiece in the series, which will help New Zealand and Bangladesh prepare for the ICC Champions Trophy in England.
"Gone are the days, we hope, of being starved of the matches we deserve," said Cricket Ireland's Warren Deutrom.
Dates and venues for the series - in May 2017 - are yet to be confirmed.
"Rather than getting nine or 10 ODIs in the four years between World Cups, we aim to play at least that number annually," added chief executive Deutrom.
"For years now, we have been asking for more matches to test our players, to raise the profile of our sport, to bring in new fans, and to attract more investment."
Ireland have a busy schedule of home fixtures arranged for this summer, with two games against Sri Lanka in June, a five-match series against Afghanistan in Belfast in July plus two encounters with Pakistan in August.
The Irish will also take on South Africa and Australia in South Africa in late September.
Earlier this week, the ICC announced it had given both Ireland and Afghanistan more than £340,000 to help the two countries arrange more matches as they attempt to improve their world ranking and secure places at the 2019 World Cup.
Next year's New Zealand games will see Ireland coach John Bracewell face his native country.
"We are now getting the volume of cricket that the team needs to take their cricket to the next level," he said.
"With home advantage in at least 13 ODIs we'll certainly have plenty of opportunities to test ourselves against quality opposition."
Ireland defeated Bangladesh at the 2007 World Cup but then lost against them four years later in India.
The Irish lost their first one-day international against New Zealand at the 2007 World Cup in Guyana and were beaten again in their only other meeting in Aberdeen a year later.
England players will not be allowed to miss Test matches to play in the Indian Premier League, says director of cricket Andrew Strauss.
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Ireland will host New Zealand and Bangladesh in a one-day tri-series next year as they continue their efforts to play more games against full members.