The Italian club have already spent big this window and had registered an interest in signing Alonso on loan with an option to buy.
Alonso, who is out of favour at Chelsea after falling out with boss Frank Lampard last week, is seeking to leave Stamford Bridge, and the Spain international was targeted by Antonio Conte's Inter, having also been of interest in January.
Conte had been interested in bringing in fellow left-back Emerson Palmieri from Chelsea on a similar deal, with Inter only needing to sign one this summer having agreed a deal to bring in Matteo Darmian from Parma.
However, Marotta has confirmed that Alonso will not be heading to San Siro before the transfer window closes, telling DAZN: "I can say that [Alonso] is not on our agenda and so he will not arrive."
Inter have also been busy in terms of outgoing activity since the end of last season by moving on a number of fringe players, with Nainggolan expected to be next out of the door.
Marotta added: "We cannot keep a player [Nainggolan] who wants to leave. This will be evaluated with all members of the club."
Cagliari coach Eusebio Di Francesco has confirmed that Nainggolan is keen to return to the club, but is also hoping for further new signings before Monday's deadline.
“Nainggolan is an Inter player, even if he wants to return here and we want him back,” said Di Francesco after a 5-2 away defeat at Atalanta.
“I think we need more new signings to boost the team in other departments."
Inter, meanwhile, took maximum points from their first two matches and Marotta feels they are a better side than they were 12 months ago.
"In this market we have strengthened," he said shortly before Inter's clash with Lazio on Sunday. "We have spent a year that has led to this and we feel stronger."