Sporting director Deco had offered to send Balde to Milan in exchange for Dimarco, with Barcelona also willing to add a cash sweetener to get the deal done, according to Sport.
Inter Milan's response left little room for negotiation: the club's hierarchy regard Dimarco as indispensable to the squad and have no intention of losing him with the window just days from closing.
The idea stemmed partly from Balde's complicated start to the season. The 22-year-old was left out of Barcelona's opening squad against Elche and, when recalled for the following match against Athletic Club, did not play a single minute.
Hansi Flick has since called on him publicly to show greater focus and consistency if he wants to force his way back into the side. Despite the pressure, Balde has told the club he wants to stay and fight for his place.
Competition for the left-back spot has intensified sharply this summer, with João Cancelo's arrival and the emergence of teenager Xavi Espart both eating into Balde's game time. Faced with that logjam, Barcelona had been prepared to sacrifice him if it meant bringing in a player of Dimarco's calibre, but Inter's immediate refusal to even discuss letting the Italy international go has closed off that route, reaffirming their full confidence in him and taking any swap scenario off the table.
Barring a dramatic change of heart, the deal is not expected to progress in the closing hours of the window.
Balde's situation remains unresolved regardless: Manchester United and AC Milan have both made contact over his availability in recent weeks, with Milan's interest reportedly contingent on finding a workable loan or instalment-based structure rather than an outright fee, while a permanent United bid is said to be valued in the region of €40m.
For now, though, Balde's stated preference to remain and battle for a starting role means Barcelona are unlikely to force through a sale before Tuesday's deadline unless the picture changes significantly.