The 25-year-old was left out of the last two Tests against India but returned for the final two One-day games last month.
"We realised that Sami needs some confidence-building as he clearly lacked it. He will definitely be considered for the Test team to be announced after the One-dayers," Bari said.
Sami has taken 65 wickets in 25 Tests and 109 in 76 One-day internationals, figures which experts say belie his huge potential.
Another frontline pacer, Shaoib Akhtar, was earlier ruled out of the tour as he has been recuperating from surgery on both knees last week.
Veteran off-spinner Arshad Khan was also left out to make room for two uncapped players, off-spinning allrounder Tahir Khan and left-arm spinner Abdul Rehman.
The 25-year-old Tahir has performed well for Karachi while 26-year-old Rehman is also an outstanding fielder.
"The two newcomers are included in the One-day team keeping in mind that we have to build the squad for next year's World Cup," said Bari.
The Pakistani team will fly out to Sri Lanka on Sunday and play the first of three One-day matches in Colombo on March 17.
The remaining two limited overs internationals, also in Colombo, are scheduled for March 19 and 21.
The first Test starts in Colombo on March 24 and the second at Kandy on April 1.
Pakistan: Inzamam-ul-Haq (capt), Salman Butt, Imran Farhat, Shoaib Malik, Younis Khan, Mohammad Yousuf, Faisal Iqbal, Shahid Afridi, Kamran Akmal, Abdul Razzaq, Danish Kaneria, Rana Naved-ul-Hasan, Mohammad Asif, Rao Iftikhar, Abdul Rehman, Tahir Khan, Umar Gul
Coach: Bob Woolmer. Manager: Zaheer Abbas.