Ingersoll Rand Inc. has made takeover bids for component maker SPX Flow Inc. that have so far been rebuffed, according to people familiar with the matter.

The industrial-machinery company’s most recent all-cash offer valued SPX Flow in the low-$80s a share, the people said, or around $3.5 billion. SPX shares closed Friday at $62.09, giving the company a market value of about $2.6 billion.

Charlotte, N.C.-based SPX primarily makes components for machinery used by food-and-beverage and industrial companies. Ingersoll Rand, one of the world’s largest manufacturers of industrial pumps and compressors, has a market value of about $20 billion.

In 2019, the former Ingersoll-Rand PLC, then incorporated in Dublin, agreed to merge with Gardner Denver Holdings Inc. The deal combined Gardner Denver’s selection of compressor, pump, vacuum and blower products and services with the part of Ingersoll Rand that made similar tools and systems as well as equipment for lifting and material handling, and golf carts.

The remainder of the company—heating, ventilation and air- and temperature-controlled transport businesses—became Trane Technologies PLC.

Former Gardner Denver Chief Executive Vicente Reynal has led the combined company since the deal closed in 2020. Ingersoll Rand has since sold its golf-cart business to private-equity firm Platinum Equity for around $1.7 billion.

Private-equity firm KKR & Co. owned a stake in Gardner Denver at the time of the merger and remains a more-than-7% shareholder in Ingersoll Rand, according to FactSet. It also holds seats on the board.

Write to Cara Lombardo at cara.lombardo@wsj.com and Miriam Gottfried at Miriam.Gottfried@wsj.com