Jaitley, however, declined to comment on whether Rajan's term would be extended after his current three-year tenure ends this September.
Rajan has been facing a continuous attack by BJP MP Subramanian Swamy and by some other sections, who have demanded termination of his service or at least denial of any extension while alleging the RBI Governor has failed to lower interest rates and boost the economy.
"I do not approve of any of these comments being made by anyone as far as the personality is concerned, because the RBI and its Governor is an important institution in Indian economy," Jaitley told PTI in an interview here.
The comments follow Swamy writing to Prime Minister Narendra Modi twice within a fortnight calling for sacking of Rajan even before his term comes up for renewal in September.
Swamy has also accused Rajan of keeping interest rates unnecessarily high, violating rules by criticising the government in speeches and using his Chicago University e-mail address to send "sensitive financial information" worldwide.
Asked if Government will consider a second term to Rajan, he said, "These are not the subjects, I discuss with media."
A former chief economist of the International Monetary Fund (IMF), Rajan is currently on leave from the Chicago Booth School of Business. He was appointed RBI Governor by the previous UPA government.
If denied an extension, he will be the first RBI Governor since 1992 to not have a five-year term.
Rajan, who after taking over raised the short-term lending rate from 7.25 per cent to 8 per cent and retained the high rates throughout 2014, began the process of lowering the rates in January 2015. He has since then cut them 1.50 per cent to 6.50 per cent.
