A move for the 35-year-old striker, a free agent this summer following his departure from Atletico Madrid, was being considered with boss Steven Gerrard keen to bolster his options up front.
But it is believed Villa are now looking at other targets and Suarez is no longer a viable option.
The signing of Olsen on a permanent deal from Roma for a fee of around £3million is expected to happen, after the Sweden international spent the second half of the season on loan at Villa Park.
Olsen’s only appearance came in the 3-2 final day defeat at Manchester City but the 32-year-old made a positive impact at Bodymoor Heath and is viewed as strong competition for No.1 Emi Martinez.
He would become Villa’s fourth signing of the summer following deals for Philippe Coutinho, Boubacar Kamara and Diego Carlos.
Further arrivals are desired though the pace of business is expected to slow, with the club assessing their options and switching focus to moving players out. Midfielder Morgan Sanson and wingers Anwar El Ghazi and Trezeguet are among those who will be allowed to depart, the latter having received some interest from Fenerbahce.
Gerrard is also searching for a new assistant boss after Michael Beale’s appointment as QPR’s head coach was confirmed.
The 41-year-old, who worked under Gerrard at Rangers before moving with him to Villa last November, has agreed a three-year deal at Loftus Road. Beale said: “I’ve been looking for the right opportunity and I think I have that now.”
Villa midfielder Jacob Ramsey has, meanwhile, been rewarded for his fine season with a nomination for PFA Young Player of the Year.
Ramsey, who spent time training with the senior England squad earlier this week while away with the under-21s, scored six goals in 34 appearances and signed a five-year contract in April.
Manchester City’s Phil Foden has also been nominated along with Chelsea pair Conor Gallagher and Reece James and Arsenal’s Bukayo Saka and Emile Smith Rowe.