According to the Telegraph, Sale have agreed a cut-price deal to sign Ireland worldwide fly-half Jackson, 26, while a move for centre Olding, 25, is close.
Sale Sharks have denied any interest in signing former Ulster players Paddy Jackson and Stuart Olding. Both men were acquitted of all charges in a rape trial in Belfast earlier this year.
The players had their Ulster and Ireland contracts revoked last month in the wake of a rape trial in Belfast in which they were acquited.
Jackson has played for Ireland 25 times, while Olding has four caps, but it is not expected that either player will feature at Test level again.
Protests were then held outside Ulster's stadium while several sponsors including Bank of Ireland and Vodafone voiced concerns over conduct issues raised during the trial.
Olding was rumoured to be in talks with the Exeter Chiefs, but the Premiership club also distanced themselves from signing the 25-year-old.
Later on Wednesday Sale issued the following statement: "Sale Sharks can confirm there is no substance to the rumours now circulating in relation to the signing of the two worldwide rugby players Paddy Jackson and Stuart Olding".
Sale Sharks, who are based in Greater Manchester and now sit seventh in the Aviva Premiership table, are yet to formally comment on the development.