Born in Stirling, McLennan represented Scotland at schoolboy international level and played junior football for Lochore Welfare. He joined Rangers as a 17–year-old apprentice, but after failing to break through to the first team he moved to Falkirk. McLennan's most successful spell as a player was at East Fife from 1947 to 1957. He was part of the team that won the Scottish League Cup in 1953. He played briefly for Dundee before joining Berwick Rangers as player–manager.
McLennan took over as coach of Iraq in 1975, staying for only one year. He introduced a number of relatively unknown players, including young striker Kadhim Waal, left back Adil Khudhair, forward Ahmed Subhi, Hadi Ahmed and Falah Hassan whom he moved from midfield to play up-front. At the 1976 Gulf Cup in Doha, Iraqi defeated the United Arab Emirates (4-0), Bahrain (4-1), Oman (4-0) and then Saudi Arabia 7-1, with Kadhim Waal, a 24-year-old striker the Scotsman had handed his international debut a year earlier, netting in the first 90 seconds of the match.
In the last match against Kuwait, Iraq were 2-0 up after only four minutes of the second half; however, with the Iraqis looking for a third goal, Kuwait scored two goals in two minutes and the game ended in a 2-2 draw. The result put both teams on the same number of points and meant Iraq had to play Kuwait in a play-off for the Gulf Cup – which Iraq lost 4-2 thanks to a hat-trick from Kuwaiti striker Abdul-Aziz Al-Anbari. A few weeks later the Iraqi FA, upset by the way the team had been defeated by Kuwait and how the tournament had ended, replaced McLennan with Yugoslav coach Lenko Grčić.
His last job was at the Indian club side Churchill Brothers SC, where he had two spells, the last coming in 1998.