Palleschi was born in Richmond Hill, Ontario. He began his soccer career at the college level with the Humber College Hawks, where he was named Team MVP and to CCAA All-Canadian Team in his rookie year in 2002. In 2003, he went abroad to Italy to play in the Serie C2/B with Frosinone Calcio. He made his debut on April 27, 2003 against Acireale. After a brief stint in Italy he returned to Canada to play with Vaughan Sun Devils in the Canadian Professional Soccer League. In his first season in Vaughan he featured in the CPSL Championship final, but lost 1-0 to the Brampton Hitmen. In his second season, he was Vaughan's leading goal scorer with 9 goals. In postseason he contributed two goals against the Metro Lions in 5-3 victory. In the semi-final match against Toronto Supra he scored two goals in a 4-1 victory. After trying out for the Montreal Impact he injured his shoulder forcing him to miss the majority of the 2005 CPSL season. He featured in the postseason where he recorded a hat trick in a 4-0 victory over Toronto Croatia to lead Vaughan to the Championship final for the third straight year. Where they were defeated 2-1 to Oakville Blue Devils. In 2006, he was signed by the Toronto Lynx of the USL First Division. He made his debut on April 22, 2006 against Virginia Beach Mariners in 2-0 loss. He scored his first goal against the Puerto Rico Islanders on June 18, 2006 in a 2-1 defeat. In the quarter-final match in the Open Canada Cup against the Hamilton Serbians he recorded the lone goal in a 1-0 victory. Throughout the season he assisted in the team's record 10 game undefeated streak at home, and featured the Open Canada Cup final, but lost 2-0 against Ottawa St. Anthony Italia. After the relegation of Toronto to the PDL he signed with rivals Montreal Impact. On April 21, 2007 he made his Impact debut coming on as a substitute for Mauro Biello, and as well scoring a goal. In total, Palleschi played 26 games for the Impact and scored 3 goals. He signed with Italia Shooters in the Canadian Soccer League and was appointed team captain. He recorded his first goal of the season on May 30, 2008, against TFC Academy in 2-0 victory at home. The Shooters won their second International Division title. In the playoff run the Shooters advanced to the semifinals, but they were defeated by eventual champions Serbian White Eagles in the semi-final match. In 2014, he played in the Ontario Soccer League with the Richmond Hill Madrid where he finished as the top goalscorer in the Central Premier division and was named MVP.
